statistics phd books

Top Ten Statistics Books for Graduate Students

Learning Statistics – Beyond the Classroom

Are you genuinely interested in learning statistics and the all-important theories behind them? Enroll in an online applied statistics degree program . Master’s degree programs include books on statistics that are required or recommended by instructors – and which are handy to keep for future reference. Check out our book list, below, to supplement learning if you’re currently enrolled, or if you are looking for a refresh in various statistical areas.

The list highlights the best statistics books for graduate students and the best statistics books, in general, using recommendations based on reviews, sales, and author credentials.

The Best Books on Statistics

1. An Introduction to Statistical Learning: with Applications in R by Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani

Lead author Gareth James is currently the Interim Dean of the Marshall School of Business at the University of South Carolina and is recognized as an expert on statistical methodology. The book, recommended by Quartz , Good Reads , Book Scrolling , and Wall Street Mojo , includes the following:

• Assessing model accuracy
• An introduction to R (open source programming specifically for the social sciences)
• Linear regression (simple and multiple)
• Classification (logistic regression, linear discriminant analysis)
• Resampling methods

2. Naked Statistics: Stripping the Dread from the Data by Charles Wheelan

Wheelan is a senior lecturer and policy fellow at the Rockefeller Center at Dartmouth and a correspondent for The Economist . Wheelen states that he designed the book to apply statistical concepts to everyday life situations (e.g., how does polling work).

3. The Elements of Statistical Learning: Data Mining, Inference, and Prediction by Trevor Hastie, Robert Tibshirani, and Jerome Friedman

Two of the authors, Hastie and Tibshirani, co-authored An Introduction to Statistical Learning: with Applications in R . Lead author Trevor Hastie is a statistics professor at Stanford University. The book includes:

• Supervised learning
• Basis expansions and regularization (for non-linear relationships)
• Kernel smoothing methods

4. All of Statistics: A Concise Course in Statistical Inference by Larry Wasserman

Wasserman is a professor in the Department of Statistics and the Machine Learning Department at Carnegie Mellon University. Recommended by both Book Scrolling and Book Authority, this book is an exhaustive view of statistical concepts. It is also the winner of the 2005 DeGroot prize (which is an honor awarded for outstanding statistical books).

5. Head First Statistics: A Brain-Friendly Guide by Dawn Griffiths

Griffiths is a mathematician and computer scientist who has written a series of “Head First” books. This series makes use of learning techniques such as visuals and activities. Reviewers note the straightforward approach to breaking down the fundamentals of statistics in lay language.

6. Principles of Statistics by MG Bulmer

Bulmer is a biostatistician and Fellow of the Royal Society of London, and an Emeritus Fellow of Wolfson College, Oxford. The original publication dates back to 1965 and remains popular. Good Reads indicates that this book remains distinctive in bridging statistical theory with practical application. The intent of this book is to enhance understanding of the concepts acquired in statistical courses.

7. Statistical Inference by George Casella, Roger L. Berger

Casella (1951-2012) was a distinguished professor in the Department of Statistics at the University of Florida. This highly recommended book breaks down the theories in statistics for increased comprehension. Intended for graduate students, it is noted as a handy reference book.

8. Statistics by David Freedman, Robert Pisani, Roger Purves

Freedman (1938-2008) was a mathematical statistician and a statistics professor at the University of California, Berkeley. This book covers such topics as:

• Controlled experiments
• Observational studies
• Descriptive Statistics
• Correlation and Regression

Sampling, in particular, can be underemphasized in many texts, and it’s covered thoroughly in this one.

9. Statistics by Robert Witte, John Witte

Robert Witt, a psychology professor, taught statistics for over thirty years. John Witte is an epidemiology and biostatistics professor at the University of California, San Francisco. This particular text goes in-depth in such classical statistical procedures as:

• t-Test (one sample, independent samples, related samples)
• Analysis of Variance (ANOVA) (One and Two Factors)
• Tests for Ranked (Ordinal) Data

Given the popularity of surveys with many using Likert (ordinal) scales, the section on appropriate tests for such data makes this book a must for analysts.

Last on the list of best statistics books is the primer of data visualization – another important aspect of statistics:

10. The Visual Display of Quantitative Information by Edward Tufte

Tufte is recognized as a pioneer in the field of data visualization and has been referred to as “the Da Vinci of Data.” Tufte delves into graphical practice and the theory of data graphics. Particularly noteworthy is the section entitled “chartjunk,” which goes over many common mistakes made when attempting to tell a story with data. Also included are various designs for displaying information.

Best Use of the Best Statistics Books

Most, if not all, of these books, are best used as supplements and enhancements for those enrolled in (or graduates of) advanced degree programs in statistics. Anyone interested in learning statistics should consider Michigan Technological University’s Online Masters in Applied Statistics program . This entirely online program is particularly useful for those looking to integrate statistics and analytics into their organizations. This program is a great way to further your education and career – enjoy your reading!

Top Skills Needed by Statisticians

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Recommended texts

1. applied and theoretical statistics, categorical data.

• ‘‘Categorical Data Analysis’’ by Alan Agresti Well-written, go-to reference for all things involving categorical data.

Causal Inference

More information available through the causal inference reading group and online seminar

Communicating with Data

• ‘‘Communicating with Data The Art of Writing for Data Science’’ by Deborah Nolan and Sara Stoudt

Compositional Data

• ‘‘Compositional Data Analysis’’ by Pawlowsky-Glahn and Buccianti

Linear models

• ‘‘Generalized Linear Models’’ by McCullagh and Nelder Theoretical take on GLMs. Does not have a lot of concrete data examples.
• ‘‘Statistical Models’’ by David A. Freedman Berkeley classic!
• ‘‘Linear Models with R’’ by Julian Faraway Undergraduate-level textbook, has been used previously as a textbook for Stat 151A. Appropriate for beginners to R who would like to learn how to use linear models in practice. Does not cover GLMs.

Experimental Design

• ‘‘Design of Comparative Experiments’’ by Rosemary A Bailey Classic, approachable text, free for download here

Machine Learning (see also Probabilistic Modeling and Sampling)

• ‘‘The Elements of Statistical Learning’’ by Hastie, Tibshirani, and Friedman Comprehensive but superficial coverage of all modern machine learning techniques for handling data. Introduces PCA, EM algorithm, k-means/hierarchical clustering, boosting, classification and regression trees, random forest, neural networks, etc. …the list goes on. Download the book here .
• ‘‘Computer Age Statistical Inference: Algorithms, Evidence, and Data Science’’ by Hastie and Efron.
• ‘‘Pattern Recognition and Machine Learning’’ by Bishop
• ‘‘Bayesian Reasoning and Machine Learning’’ by Barber Available online .
• ‘‘Probabilistic Graphical Models’’ by Koller and Friedman
• ‘‘Deep Learning’’ by Goodfellow, Bengio and Courville

Multiple Testing, Post-Selection Inference and Selective Inference

• ‘‘Multiple Comparisons: theory and methods’’ by Jason Hsu One of many sources in this field of research. Most of the literature comes from research papers.

More information available through online seminar .

Probabilistic Modeling and Sampling (see also Machine Learning)

• ‘‘Monte Carlo Statistical Methods’’ by Robert and Casella A comprehensive text on sampling approaches.
• ‘‘Handbook of Approximate Bayesian Computation’’ by Sisson, Fan and Beaumont
• ‘‘Graphical Models, Exponential Families, and Variational Inference’’ by Wainwright and Jordan Assuming knowledge at the level of Stat 210AB, elucidates how exponential families can be used in large-scale and interpretable probabilistic modeling.

Theory and Foundations

• ‘‘Theoretical Statistics: Topics for a Core Course’’ by Keener The primary text for Stat 210A. Download from SpringerLink .
• ‘‘Theory of Point Estimation’’ by Lehmann and Casella A good reference for Stat 210A, covering estimation.
• ‘‘Testing Statistical Hypotheses’’ by Lehmann and Romano A more advanced reference for Stat 210A, convering testing and a litany of related concepts.
• ‘‘Empirical Processes in M-Estimation’’ by van de Geer
• Some students find this helpful to supplement the material in 210B.
• ‘‘Concentration Inequalities’’ by Boucheron, Lugosi, and Massart This is also useful to supplement 210B material.

2. Probability

Undergraduate level probability.

• ‘‘Probability’’ by Pitman What the majority of Berkeley undergraduates use to learn probability.
• ‘‘Introduction to Probability Theory’’ by Hoel, Port and Stone This text is more mathematically inclined than Pitman’s, and more concise, but not as good at teaching probabilistic thinking.
• ‘‘Probability and Computing’’ by Upfal and Mitzenmacher What students in EECS use to learn about randomized algorithms and applied probability.

Measure Theoretic Probability

• ‘‘Probability: Theory and Examples’’ by Durrett This is the standard text for learning measure theoretic probability. Its style of presentation can be confusing at times, but the aim is to present the material in a manner that emphasizes understanding rather than mathematical clarity. It has become the standard text in Stat 205A and Stat 205B for good reason. Online here .
• ‘‘Foundations of Modern Probability’’ by Olav Kallenberg This epic tome is the ultimate research level reference for fundamental probability. It starts from scratch, building up the appropriate measure theory and then going through all the material found in 205A and 205B before powering on through to stochastic calculus and a variety of other specialized topics. The author put much effort into making every proof as concise as possible, and thus the reader must put in a similar amount of effort to understand the proofs. This might sound daunting, but the rewards are great. This book has sometimes been used as the text for 205A.
• ‘‘Probability and Measure’’ by Billingsley This text is often a useful supplement for students taking 205 who have not previously done measure theory. Download here .
• ‘‘Probability with Martingales’’ by David Williams This delightful and entertaining book is the fastest way to learn measure theoretic probability, but far from the most thorough. A great way to learn the essentials.

Stochastic Calculus

Stochastic Calculus is an advanced topic that interested students can learn by themselves or in a reading group. There are three classic texts:

• ‘‘Continuous Martingales and Brownian Motion’’ by Revuz and Yor
• ‘‘Diffusions, Markov Processes and Martingales (Volumes 1 and 2)’’ by Rogers and Williams
• ‘‘Brownian Motion and Stochastic Calculus’’ by Karatzas and Shreve

Random Walk and Markov Chains

These are indispensable tools of probability. Some nice references are

• ‘‘Markov Chain and Mixing Times’’ by Levin, Peres and Wilmer. Online here .
• ‘‘Markov Chains’’ by Norris Starting with elementary examples, this book gives very good hints on how to think about Markov Chains.
• ‘‘Continuous time Markov Processes’’ by Liggett A theoretical perspective on this important topic in stochastic processes. The text uses Brownian motion as the motivating example.

3. Mathematics

Convex optimization.

• ‘‘Convex Optimization’’ by Boyd and Vandenberghe. Download the book here
• ‘‘Introductory Lectures on Convex Optimization’’ by Nesterov.

Linear Algebra

• ‘‘The Matrix Cookbook’’ by Petersen and Pedersen: ‘‘Matrix identities, relations and approximations. A desktop reference for quick overview of mathematics of matrices.’’ Download here .
• ‘‘Matrix Analysis’’ and ‘‘Topics in Matrix Analysis’’ by Horn and Johnson Second book is more advanced than the first. Everything you need to know about matrix analysis.

Convex Analysis

• ‘‘A course in Convexity’’ by Barvinok. A great book for self study and reference. It starts with the basis of convex analysis, then moves on to duality, Krein-Millman theorem, duality, concentration of measure, ellipsoid method and ends with Minkowski bodies, lattices and integer programming. Fairly theoretical and has many fun exercises.

Measure Theory

• ‘‘Real Analysis and Probability’’ by Dudley Very comprehensive.
• ‘‘Probability and Measure Theory’’ by Ash Nice and easy to digest. Good as companion for 205A

Combinatorics

• ‘‘Enumerative Combinatorics Vol I and II’’ by Richard Stanley. There’s also a course on combinatorics this semester in the math department called Math249: Algebraic Combinatorics. Despite the scary “algebraic” prefix it’s really fun. Download here .

4. Computational Biology

‘big picture’ overview.

• ‘‘Modern Statistics for Modern Biology’’ by Susan Holmes and Wolfgang Huber Accessible ‘data analysis’-focused overview of the field, with numerous motivating examples and plentiful opportunities for hands-on practice. Although written for biologists, can indirectly help with developing an understanding of how to identify problems that impact on biology.

Bioinformatics

• ‘‘Statistical Methods in Bioinformatics’’ by Ewens and Grant Great overview of sequencing technology for the unacquainted.
• ‘‘Computational Genome Analysis: An Introduction’’ by Deonier, Tavaré, and Waterman Great R code examples from computational biology. Discusses the basics, such as the greedy algorithm, etc.

Population Genetics

• ‘‘Probability Models for DNA Sequence Evolution’’ by Rick Durrett
• ‘‘Mathematical Population Genetics’’ by Warren Ewens

5. Computer Science

Numerical analysis.

• ‘‘Numerical Analysis’’ by Burden and Faires This book is a good overview of numerical computation methods for everything you’d need to know about implementing most computational methods you’ll run into in statistics. It is filled with pseudo-code but does use Maple as it’s exemplary language sometimes. It has been a great resource for the Computational Statistics courses (243/244). Depending on what happens with this course, this may be a good place to look when you’re lost in computation.
• ‘‘Introduction to Algorithms’’, Third Edition, by Cormen, Leiserson, Rivest, and Stein. MIT OpenCourseWare 6.046J / 18.410J ‘‘Introduction to Algorithms’’ (SMA 5503) was taught by one of the authors, Prof. Charles Leiserson, in 2005. This is an undergraduate course and this book was used as the textbook
• ‘‘Algorithm Design’’, by Jon Kleinberg and Éva Tardos.

Statistics for Research Students

(2 reviews)

Erich C Fein, Toowoomba, Australia

John Gilmour, Toowoomba, Australia

Tayna Machin, Toowoomba, Australia

Liam Hendry, Toowoomba, Australia

Copyright Year: 2022

ISBN 13: 9780645326109

Publisher: University of Southern Queensland

Language: English

Formats Available

Conditions of use.

Learn more about reviews.

Reviewed by Sojib Bin Zaman, Assistant Professor, James Madison University on 3/18/24

From exploring data in Chapter One to learning advanced methodologies such as moderation and mediation in Chapter Seven, the reader is guided through the entire process of statistical methodology. With each chapter covering a different statistical... read more

Comprehensiveness rating: 5 see less

From exploring data in Chapter One to learning advanced methodologies such as moderation and mediation in Chapter Seven, the reader is guided through the entire process of statistical methodology. With each chapter covering a different statistical technique and methodology, students gain a comprehensive understanding of statistical research techniques.

Content Accuracy rating: 5

During my review of the textbook, I did not find any notable errors or omissions. In my opinion, the material was comprehensive, resulting in an enjoyable learning experience.

Relevance/Longevity rating: 5

A majority of the textbook's content is aligned with current trends, advancements, and enduring principles in the field of statistics. Several emerging methodologies and technologies are incorporated into this textbook to enhance students' statistical knowledge. It will be a valuable resource in the long run if students and researchers can properly utilize this textbook.

Clarity rating: 5

A clear explanation of complex statistical concepts such as moderation and mediation is provided in the writing style. Examples and problem sets are provided in the textbook in a comprehensive and well-explained manner.

Consistency rating: 5

Each chapter maintains consistent formatting and language, with resources organized consistently. Headings and subheadings worked well.

Modularity rating: 5

The textbook is well-structured, featuring cohesive chapters that flow smoothly from one to another. It is carefully crafted with a focus on defining terms clearly, facilitating understanding, and ensuring logical flow.

Organization/Structure/Flow rating: 5

From basic to advanced concepts, this book provides clarity of progression, logical arranging of sections and chapters, and effective headings and subheadings that guide readers. Further, the organization provides students with a lot of information on complex statistical methodologies.

Interface rating: 5

The available formats included PDFs, online access, and e-books. The e-book interface was particularly appealing to me, as it provided seamless navigation and viewing of content without compromising usability.

Grammatical Errors rating: 5

I found no significant errors in this document, and the overall quality of the writing was commendable. There was a high level of clarity and coherence in the text, which contributed to a positive reading experience.

Cultural Relevance rating: 5

The content of the book, as well as its accompanying examples, demonstrates a dedication to inclusivity by taking into account cultural diversity and a variety of perspectives. Furthermore, the material actively promotes cultural diversity, which enables readers to develop a deeper understanding of various cultural contexts and experiences.

In summary, this textbook provides a comprehensive resource tailored for advanced statistics courses, characterized by meticulous organization and practical supplementary materials. This book also provides valuable insights into the interpretation of computer output that enhance a greater understanding of each concept presented.

Reviewed by Zhuanzhuan Ma, Assistant Professor, University of Texas Rio Grande Valley on 3/7/24

The textbook covers all necessary areas and topics for students who want to conduct research in statistics. It includes foundational concepts, application methods, and advanced statistical techniques relevant to research methodologies. read more

The textbook covers all necessary areas and topics for students who want to conduct research in statistics. It includes foundational concepts, application methods, and advanced statistical techniques relevant to research methodologies.

The textbook presents statistical methods and data accurately, with up-to-date statistical practices and examples.

Relevance/Longevity rating: 4

The textbook's content is relevant to current research practices. The book includes contemporary examples and case studies that are currently prevalent in research communities. One small drawback is that the textbook did not include the example code for conduct data analysis.

The textbook break down complex statistical methods into understandable segments. All the concepts are clearly explained. Authors used diagrams, examples, and all kinds of explanations to facilitate learning for students with varying levels of background knowledge.

The terminology, framework, and presentation style (e.g. concepts, methodologies, and examples) seem consistent throughout the book.

The textbook is well organized that each chapter and section can be used independently without losing the context necessary for understanding. Also, the modular structure allows instructors and students to adapt the materials for different study plans.

The textbook is well-organized and progresses from basic concepts to more complex methods, making it easier for students to follow along. There is a logical flow of the content.

The digital format of the textbook has an interface that includes the design, layout, and navigational features. It is easier to use for readers.

The quality of writing is very high. The well-written texts help both instructors and students to follow the ideas clearly.

The textbook does not perpetuate stereotypes or biases and are inclusive in their examples, language, and perspectives.

Table of Contents

• Acknowledgement of Country
• Accessibility Information
• About the Authors
• Introduction
• I. Chapter One - Exploring Your Data
• II. Chapter Two - Test Statistics, p Values, Confidence Intervals and Effect Sizes
• III. Chapter Three- Comparing Two Group Means
• IV. Chapter Four - Comparing Associations Between Two Variables
• V. Chapter Five- Comparing Associations Between Multiple Variables
• VI. Chapter Six- Comparing Three or More Group Means
• VII. Chapter Seven- Moderation and Mediation Analyses
• VIII. Chapter Eight- Factor Analysis and Scale Reliability
• IX. Chapter Nine- Nonparametric Statistics

Ancillary Material

About the book.

This book aims to help you understand and navigate statistical concepts and the main types of statistical analyses essential for research students. 

About the Contributors

Dr Erich C. Fein  is an Associate Professor at the University of Southern Queensland. He received substantial training in research methods and statistics during his PhD program at Ohio State University.  He currently teaches four courses in research methods and statistics.  His research involves leadership, occupational health, and motivation, as well as issues related to research methods such as the following article: “ Safeguarding Access and Safeguarding Meaning as Strategies for Achieving Confidentiality .”  Click here to link to his  Google Scholar  profile.

Dr John Gilmour  is a Lecturer at the University of Southern Queensland and a Postdoctoral Research Fellow at the University of Queensland, His research focuses on the locational and temporal analyses of crime, and the evaluation of police training and procedures. John has worked across many different sectors including PTSD, social media, criminology, and medicine.

Dr Tanya Machin  is a Senior Lecturer and Associate Dean at the University of Southern Queensland. Her research focuses on social media and technology across the lifespan. Tanya has co-taught Honours research methods with Erich, and is also interested in ethics and qualitative research methods. Tanya has worked across many different sectors including primary schools, financial services, and mental health.

Dr Liam Hendry  is a Lecturer at the University of Southern Queensland. His research interests focus on long-term and short-term memory, measurement of human memory, attention, learning & diverse aspects of cognitive psychology.

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The 14 Best Statistics Books for Data Science

Statistics and data science are among the most challenging subjects to self-learn. If you have never had experience in any of these two fields, you will need to be ready to put time and commitment to learning these always-evolving disciplines. However, in this process, picking the right volumes and textbooks is essential. 

The best statistics books for Data Science include Naked Statistics: Stripping the Dread from the Data by Charles Wheelan and Practical Statistics for Data Scientists – Peter Bruce. To learn more about stats in R, read Discovering Statistics Using R – A. Field, J. Miles, and Z. Field.

Find out more about the best books to learn statistics from scratch and become a skilled data scientist .

Important Sidenote: We interviewed numerous data science professionals (data scientists, hiring managers, recruiters – you name it) and identified 6 proven steps to follow for becoming a data scientist. Read my article: ‘6 Proven Steps To Becoming a Data Scientist [Complete Guide] for in-depth findings and recommendations! – This is perhaps the most comprehensive article on the subject you will find on the internet!

Table of Contents

Are Books Effective to Learn Statistics for Data Science?

Textbooks and specialized training sessions have been used in university courses to improve the quality of the teaching. However, if you are trying to learn statistics from scratch to become a data scientist , be aware that there are significant limitations presented by textbooks. 

• Data Science, as stated in several Forbes articles, is a relatively new field , in which innovations happen every day and developments are carried out continuously. Consequently, only a few staple books can be useful to understand the basic concepts of this discipline. Therefore, if you are looking for some recent research or innovation, you are better off consulting the internet or journals on the field. 
• If you are not sure about what data science entails , there is always the danger of getting lost in the myriad of information that composes the field of statistics. While the majority of concepts are also the pillars at the core of the field of Data Science, some other concepts might not be so relevant when you are looking for a job in data science. 
• Statistics are considered among the most challenging subjects to self-learn using only volumes and textbooks. Therefore, you will need to be well-equipped with patience, commitment, constancy, and willingness to go over some more complicated subjects a few times. 

While it is easy to get discouraged, keep in mind that it is normal to find some challenges when studying a field so complicated and in evolution like data science or statistics can be. Additionally, using other learning methods and tools such as online videos and training can help you understand some concepts easier and faster.

Statistics – Robert S. Witte and John S. Witte

If you wish to approach the field of statistics and you have no previous experience in the field, this is a suitable book for you. 

The 11th edition of this volume has been released, and you can find updated information and latest innovation alongside staple principles and concepts of statistics.

In terms of knowledge level, you can expect to grow from a beginner level to an undergraduate level. The journey is assisted by the organized chapter, easy-to-understand text, and clear graphs. 

While this book is perfect if you are just starting your studies, many professionals opt to use it as a backup reference for certain projects.

Among the most important features of this book is the fact that every jargon and obscure terms are explained in detail. Some of the concepts covered include variations of coefficient and correlation, interpretation, and hypothesis.

• Accessibility: available online, the price varies from over $170 to $21 (for the eBook)
• Experience level: Beginner
• Best for: learners interested in the basics of statistics. It focuses on basic principles and essential concepts.
• Find it here in the eBook format: Statistics, 11th Edition  

Barron’s AP Statistics, 8th Edition – Martin Sternstein, PhD

Written by the head of various math departments in Universities, the Barron’s AP Statistics volume focuses primarily on the connection between math and statistics. 

Of course, mathematical algorithms and calculations are at the core of this field as well as data science. However, other books only focus on one aspect, excluding some of the basics of math. 

This affordable book is also easy to read and highly accessible. Inside, you will find 15 chapters – one for each basic concept of statistics. While some might not be covered particularly in-depth, you can get an all-around knowledge of a subject.

If you would like to practice, this book includes a CD to watch and tests that you should be able to pass at the end of every chapter. Answers to the questions are also included to enable self-learning.

• Accessibility: available online at the cost of around $9. On eBay, you can find cheaper second-hand versions.
• Experience level: beginners and experts looking at specializing 
• Best for: beginner statisticians interested in the link between math and statistics

Statistics for Business and Economics – James T. McClave, P. George Benson and Terry T. Sincich

This book is the brainchild of a series of experts in the fields of math, finances, market trends, and statistics. Unlike the option seen above, this book primarily focuses on the applications that statistics find in the world of business and economics. 

The fact that the authors have brought their own experience into the making of this book offers students the opportunity to work with real-world examples and truthful reports. You can find traces of these stories in the example used, as well as in tests and exercises. 

Another aspect of Statistics for Business and Economics worth mentioning is the fact that this book is organized in easy-to-read chapters that revolve around a relevant case study. These real-world instances are used to explain a new concept of statistics to the students.

One of the main advantages of this type of learning technique is that you are likely to find the content more motivating and engaging. This is not always true in the case of statistics books that don’t refer so much to real-life scenarios and practical applications.

• Accessibility: available in a range of formats, with prices varying from $10 to $150
• Experience level: beginner and intermediate
• Best for: statistic students interested in business application and real-world data

Naked Statistics: Stripping the Dread From the Data – Charles Wheelan

If you have been waiting to find a book that would make you fall in love with statistics, at first sight, you have found it. This book is a little irreverent, and it has a unique point of view over the always-considered serious and monotone field.

Funny and accessible, this book is created to be an optimal choice for everybody, whether you are a navigated student, amateur statistician, or just curious about a field that can open so many career opportunities.

While using real-world examples and easy-to-read chapters, this relatively small volume works perfectly for everybody who is looking for an alternative introduction to statistics. 

Of course, you might need to complement this book with another, more in-depth volume that can explain in more detail some main topics. However, if you were not sure whether statistics is the field for you or not, Naked Statistics can give you an immediate answer!

• Accessibility: it is available online, with a cost ranging between $7 and $9. You can also opt for the free Audible version.
• Experience level: beginners, curious
• Best for: students interested in the real-world application of statistics with a fun twist.

Practical Statistics for Data Scientists – Peter Bruce

The complete title of this book is Practical Statistics for Data Scientists: 50+ Essential Concepts Using R and Python. This headline says a lot about how useful this modern volume could be when starting out your career in data science .

While focusing on the notions of data science and the use of R, this book brings the attention of the readers on the fact that not many data scientists have formal training in statistics . Nonetheless, this whole discipline is founded in the field of statistics.

Instead, this book starts with the statistical concepts and tells you what the best use you could make of them in the field of data science. The chapters cover:

• Importance of exploratory data in data science
• Random sampling
• Experimental design’s principles
• Detection of anomalies
• Statistical machine learning methods 
• Unsupervised learning methods

These are just among the concepts you will learn in this book, but several of the chapters explore in-depth other techniques that can be used in Data Science.

• Accessibility: around $40 if bought online. There is also a free version available in PDF format if you don’t feel like committing to a significant expense.
• Experience level: beginner-intermediate. Knowledge of R preferred
• Best for: Statisticians who are looking at using Python and R
• Free PDF: Practical Statistics for Data Scientists  

Head First Statistics: A Brain-Friendly Guide – Dawn Griffiths

One of the selling points of this accessible volume is the fact that it tries to make fun and to entertain a subject such as statistics – and it succeeds in it. Firstly, you will be able to find simplified concepts and explanations of jargon and acronyms. 

Alone, these two characteristics would be enough for you to move onto your studies further. However, this book does not stop here. Indeed, reading the different chapters, you will explore all the major concepts of statistics, including the ones that are the most suitable for data science projects.

The puzzles, visual aids, case studies, and real-world examples included in this book make sure it fits in the top more interesting books to learn statistics for data science. 

• Accessibility: online cost varying between $7 and $23
• Experience level: beginners
• Best for: students interested in concepts but not in terms and jargon

Introduction to Statistical Learning – Gareth James

If you are looking for a complete, all-encompassing introduction to the field of Statistical Learning, this volume is the right one for you. However, the book focuses on the explanations of how to use large data sets to allow a pattern to emerge. 

Therefore, if you want to launch a career in data science, this book should already be in your shopping cart.

Inside, you will be able to find real-world examples, graphs, charts, and case studies that can help simplify even the most complex concept. R – the preferred programming language by data scientists – is used for the analysis of certain situations, so you have a complete toolkit to start practicing in the field.

• Accessibility: the cost varies depending on the format and can be as high as $50. The volume is also available on Springer.
• Experience level: beginner, but linear regression knowledge is assumed
• Best for: students with a basic level of mathematical knowledge

Think Stats – Allen Downey

Think Stats is a modern, easy-to-read book that can help you refine your skill as a statistician and data scientist. This book focuses on the use of programming languages such as R and Python to perform tasks such as statistical analysis instead of completing the process mathematically.

To have an all-encompassing knowledge of the process. This book uses a single case study throughout the book. This case study will show you how to gather the data, analyze them, and draw conclusions from them.

Since you will be using real-world data during your training, you will also acquire some statistical knowledge that is useful in data science.

• Accessibility: between $20 and $40
• Experience level: beginner statisticians with experience in computing sciences or programming. Knowledge of coding and programming is assumed.
• Best for: students who want to upgrade their skills and use statistics within their current project.

All of Statistics: A Concise Course in Statistical Inference – Larry A. Wasserman

It is not exactly as the title of the book says – it does not cover all of the statistics. It is fair to say that this statistical book helps you discover a much greater range of concepts than most other introductory books, but it might not show you an in-depth look of all the characteristics of certain models and notions.

If you are already familiar with statistical aspects, reading this book can broaden your career-related horizon. Moreover, unlike other more traditional books about stats, this volume includes the latest innovations and the most modern upgrades on staple concepts of statistics.

• Accessibility: parts available on SpringerLink. The whole volume is accessible for minimal cost.
• Experience level: introductory book on mathematical statistics
• Best for: beginners 

Statistics – David A. Freedman

While not among the most recent books on statistics, this volume contains basic notions and staple concepts that are useful in many fields. 

Whether you wish to take your education further and specialize in data science or you wish to pursue a project’s research, this book will give you all the fundamentals you need to face most tasks.

If you are worried about the lack of new concepts and innovations, keep in mind that new editions are released regularly for the benefits of students and professionals alike.

• Accessibility: free PDF version available. Otherwise, it can cost between $50 and $100.
• Best for: beginners who are looking to cover all the main concepts of statistics

Innumeracy: Mathematical Illiteracy and Its Consequences – John Allen Paulos

First published in 1988, this bestseller asks why it is important to understand mathematical and statistical sciences. 

In the pages of Innumeracy, you will be able to find out about the consequences of innumeracy and the benefits of having control over it. Mathematics and statistics are indeed used in many aspects of societies, including lotteries and insurance firms. 

Understanding how probability and trends are functioning can offer you better control over what is happening in your life.

If you know that you have always been interested in the field of statistics, but you are not sure what you will do with the knowledge acquired, go ahead and purchase this book. 

• Accessibility: available online for $4 to $7
• Experience level: beginner/curious
• Best for: someone who wants to know more about the importance of learning more about math and stats – and, of course, data science.

The Elements of Statistical Learning: Data Mining, Inference, and Prediction – Jerome H. Friedman, Robert Tibshirani, and Trevor Hastie

It is essential to understand what is the concept of statistics that you are bound to use in data science. Indeed, statistics is an extremely broad field that might include concepts not useful in other disciplines.

However, if you are looking for a book that can help you refine the skills needed for data science, the knowledge presented in this book is what you need. Indeed, many companies rely on processes such as data mining, prediction, and inference to create analytical models that can be used in real life.

Unfortunately, there is a limited number of books on the market that will be as clear as this one when explaining such complex processes. Luckily, though, a free PDF version is available for you to grab.

• Accessibility: the free PDF gives you accessibility to this resource every time you need it.
• Experience level: intermediate
• Best for: learners looking at deepening their knowledge in data mining and prediction models
• Free version: The Elements of Statistical Learning  

Discovering Statistics Using R – Andy Field, Jeremy Miles, and Zoë Field

While you won’t need to have an exhaustive knowledge of statistics to enjoy this book, it is recommendable to get to know better the functions of R. this statistical language often used by data scientists is based on a statistical language that enables programmers to leverage the speed and efficiency of a programming language and the ingenious statistical models.

Unlike many other structured books on the market today, this volume is written in a witty, irreverent tone that can help you get involved in the field more. You can also find self-assessment tests and quizzes to test your knowledge as you continue reading. 

Don’t underestimate the importance of a book written in an engaging tone, especially if the book in question is about statistics. 

• Accessibility: from $18 to $190 (for hardback cover)
• Experience level: intermediate – experience in programming and knowledge of basic concepts of stats is assumed
• Best for: using R in your career

A Probabilistic Theory of Pattern Recognition – Luc Devroye

The last book on our list is the self-contained volume written by Luc Devroye. The chapters of this book cover a huge range of techniques and statistical processes that you will be able to use when working in data science. 

Among the most important ones, you will find nearest neighbor rules, parametric classification, and feature extraction. Just like the previous book, you will be able to find tests and quizzes at the end of every section.

• Accessibility: from $70 to $180
• Experience Level: intermediate
• Best For statisticians and data scientists looking at refining their knowledge

Considerations and Features of the Best Statistics Books for Data Science

As mentioned, statistics are among the most difficult subjects to learn just by reading a book. When it comes down to applying the notion learned in such a practical and evolving field like data science, it is essential to couple up your theoretical knowledge with practical skills. 

However, if you would like to start your journey in this industry from a book, there are some critical characteristics to keep in mind. Even if you have opted for a book different from the ones mentioned above, make sure it boasts the following characteristics – you can do so by checking out the reviews on these books on platforms such as Amazon.

Easy to Understand

Firstly, a book about statistics should be easy to understand. Statistics and data science , just like other fields, use abbreviations and jargon that can make learning more about the field much more challenging. 

However, there are books that avoid such terms at first, just to explain the meaning of certain phrases, abbreviations, or common terms later on. 

Such a learning method can help you arrive at the phase in which you need to apply the notions learned fully prepared. And, when you are applying for a data science job , you will sound like a pro.

Telltale signs of the intelligibility of the book can be found in the volume’s reviews or in the introduction.

Practical Applications Opportunities

Some books are purely theoretical, which are excellent if you are looking at learning statistics for research. However, this field found its foundation on user-generated and real-world data. And these are everything aside from theoretical values.

When you need to apply such notions to data science, the need for practical uses becomes paramount. Indeed, data science is an interdisciplinary field in which data gathered by companies is used to study past trends and foresee future developments.

Making sure that your book encourages you to try the notions learned in real-life scenarios is crucial if you are looking to work for a company or business in the field of data science .

Include Calculation Tips

There is no doubt about the fact that statistics is a field based on calculations, algorithms, and math in general. But some tips can help.

As an example, you could find a book that offers a satisfactory introduction about some statistical or predictive models, without actually teaching you how to extract measurable results. 

While these books might be easy to understand at first, they might leave you without the substantial knowledge needed to put such notions into practice. 

To check whether a textbook has everything you need, look for exercises and problems to solve at the end of each chapter. And of course, it should include some tips on how to use your calculator properly. 

It Is Easily Accessible

Depending on your budget and commitment to learning more about data science , you might be willing to spend more or less on volumes, books, and resources.

However, luckily, some resources are available to all students at all times. So, instead of spending money on buying just one volume and taking a chance on it, you can have a collection of various works that you can use as a reference while entering this field as a professional.

Avoid renting or borrowing these books as having a physical reference to go back to when you have a seemingly insurmountable problem can be time- and energy-saving.

Can Be Used in Combination With Other Learning Methods

Some of the books seen above come with DVDs or CDs that can help you get some of the insights explained in the book in other forms. These methods are particularly useful for visual or auditory learners who need a reference other than a textbook. 

If the volume you have picked does not come with another learning channel, there is no need to discard it altogether. However, in this case, you might consider subscribing to platforms such as Udemy and SkillShare to deepen your knowledge and apply the notions learned.

Author’s Recommendations: Top Data Science Resources To Consider

Before concluding this article, I wanted to share few top data science resources that I have personally vetted for you. I am confident that you can greatly benefit in your data science journey by considering one or more of these resources.

• DataCamp: If you are a beginner focused towards building the foundational skills in data science , there is no better platform than DataCamp. Under one membership umbrella, DataCamp gives you access to 335+ data science courses. There is absolutely no other platform that comes anywhere close to this. Hence, if building foundational data science skills is your goal: Click Here to Sign Up For DataCamp Today!
• IBM Data Science Professional Certificate: If you are looking for a data science credential that has strong industry recognition but does not involve too heavy of an effort: Click Here To Enroll Into The IBM Data Science Professional Certificate Program Today! (To learn more: Check out my full review of this certificate program here )
• MITx MicroMasters Program in Data Science: If you are at a more advanced stage in your data science journey and looking to take your skills to the next level, there is no Non-Degree program better than MIT MicroMasters. Click Here To Enroll Into The MIT MicroMasters Program Today ! (To learn more: Check out my full review of the MIT MicroMasters program here )
• Roadmap To Becoming a Data Scientist: If you have decided to become a data science professional but not fully sure how to get started : read my article – 6 Proven Ways To Becoming a Data Scientist . In this article, I share my findings from interviewing 100+ data science professionals at top companies (including – Google, Meta, Amazon, etc.) and give you a full roadmap to becoming a data scientist.

The books mentioned above are the ones you can use to start learning statistics for data science. Every learner might prefer different methods to acquire and retain information about this ever-changing field. 

While these amazing books are well-crafted for you to get a head start in the field, don’t forget to increase your practical knowledge by subscribing to online courses or specialized training. For example, you might like to start applying the notions learned in R or increase your knowledge of useful programming languages like Python. 

Ultimately, a lot depends on the career you would like to build for yourself in this field.

BEFORE YOU GO: Don’t forget to check out my latest article – 6 Proven Steps To Becoming a Data Scientist [Complete Guide] . We interviewed numerous data science professionals (data scientists, hiring managers, recruiters – you name it) and created this comprehensive guide to help you land that perfect data science job.

• Calculator tips and tricks. (n.d.). Department of Statistics. https://statweb.stanford.edu/~dlsun/60/calc.html
• Different types of learners: What college students should know. (n.d.). Regionally Accredited College Online and on Campus | Rasmussen College.  https://www.rasmussen.edu/student-experience/college-life/most-common-types-of-learners/
• Press, G. (2014, October 15). A very short history of data science. Forbes.  https://www.forbes.com/sites/gilpress/2013/05/28/a-very-short-history-of-data-science/#7ca774f255cf
• Statistics, 11th edition. (2017, January 5). Wiley.com. https://www.wiley.com/en-us/Statistics%2C+11th+Edition-p-9781119254515
• (n.d.). Tilastokeskus. https://www.stat.fi/isi99/proceedings/arkisto/varasto/rams0070.pdf

Affiliate Disclosure: We participate in several affiliate programs and may be compensated if you make a purchase using our referral link, at no additional cost to you. You can, however, trust the integrity of our recommendation. Affiliate programs exist even for products that we are not recommending. We only choose to recommend you the products that we actually believe in.

Daisy is the founder of DataScienceNerd.com. Passionate for the field of Data Science, she shares her learnings and experiences in this domain, with the hope to help other Data Science enthusiasts in their path down this incredible discipline.

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Simplifying Statistics for Graduate Students: Making the Use of Data Simple and User-Friendly

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One of the greatest barriers to completing a graduate thesis or a doctoral dissertation is statistics. Oftentimes, the journey through graduate school is gratifying when the content courses in the chosen field of study are undertaken. Conversely, the statistics courses are met with trepidation. Many graduate students feel lost when it comes to dealing with data. Simplifying Statistics for Grad Students:Making the Use of Data Simple and User-Friendly is intended to help graduate students move through the barriers that seem formidable but are not. While this book is not a statistics text and does not purport to be such, it introduces graduate students to basic statistical concepts in an easy-to-comprehend manner. It is also a handbook that they can refer back to time and time again. Expertise with data is expected of graduate students. Simplifying Statistics for Grad Students is an antidote for the research and statistics blues.

• ISBN-10 1475868391
• ISBN-13 978-1475868395
• Publisher Rowman & Littlefield Publishers
• Publication date March 7, 2023
• Language English
• Dimensions 6 x 0.31 x 9 inches
• Print length 134 pages
• See all details

Editorial Reviews

Simplifying Statistics for Graduate Students is an excellent “Must-Have” for anyone in a graduate program The progressive organization provides an easy to comprehend, matter-of-fact way, moving from simple to complex. Completing a doctoral degree is a process and a journey. This book gives the reader a superb roadmap to success on that journey.

Graduate students often reach an impasse with their research due to statistics distress. Faculty members who provide this book Simplifying Statistics for Graduate Students as a resource in their class can help their students succeed with less stress and more confidence.

About the Author

Susan Rovezzi Carroll, PhD has provided hundreds of graduate students with advice and support on research methods and statistical procedures. She is president of Words & Numbers Research, Inc. which she founded in 1984.

David Carroll, MSW is vice president of Words & Numbers Research, Inc. He has several research publications and books to his credit and has expertise in demographic data analysis and the development of performance indicators for assessing outcomes.

Product details

• Publisher ‏ : ‎ Rowman & Littlefield Publishers (March 7, 2023)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 134 pages
• ISBN-10 ‏ : ‎ 1475868391
• ISBN-13 ‏ : ‎ 978-1475868395
• Item Weight ‏ : ‎ 7.3 ounces
• Dimensions ‏ : ‎ 6 x 0.31 x 9 inches
• #2,486 in Statistics (Books)
• #2,609 in Social Sciences Research
• #3,276 in Math Teaching Materials

About the authors

David j. carroll.

David Carroll is Vice President at Words & Numbers Research, Inc., a research consulting firm founded in 1984. He specializes in the analysis of demographic and social trends particularly as they relate to population change, women and children, and health. His expertise lies in the development of measurements that identify, describe and quantify social changes in communities, educational and health districts, and service delivery systems.

David has conducted numerous studies and evaluations that focus on the well-being of children, the economic security of women, the educational achievement gap and health equity among diverse populations.

He conceptualized, designed and empirically tested the Health Equity Index© for the Connecticut Association of Directors of Health. The HEI is a composite statistic that is used to measure and quantify the extent to which Social Determinants have a statistically significant relationship with health outcomes in a given geographic area. The Kellogg Foundation provided a 3 million dollar grant to CADH to continue this work.

Another example is Keeping Children on the Path to School Success: How is Connecticut Doing? Research consultation was provided for the development of 25 critical indicators measuring the state's progress in ensuring the school readiness of children. The work included data collection and management, analysis and reporting. Indicators were developed in: Health and Child Development; Safety and Child Welfare; Economic Stability; Early Care and Education; and Ready Schools.

Susan Rovezzi Carroll

Susan Rovezzi Carroll, PhD is president of Words & Numbers Research. She founded the research and evaluation firm in 1984. Surveys, focus groups and in-depth interviews have been conducted for public and private schools, educational associations, state education agencies, universities and colleges, educational foundations, the US Department of Education and the National Science Foundation (NSF). Clients have also been from corporate and non-profit settings.

An expert in research design, Dr. Carroll's most popular instruments are The School Report Card Series - individual questionnaires for different audiences including elementary students, middle/secondary students, parents of school aged children, teachers and staff, community taxpayers, and school alumni.

Consultation to doctoral students has been provided in research design (Chapter 3) and statistical analysis (Chapter 4). Dr. Carroll has counseled hundreds of students at an impasse in the dissertation journey to complete their degrees by sorting out their research methodology and helping with their quantitative analysis of data sets using SPSS. (Link is www.dissertation-statistics.com)

Dr. Carroll received her Ph.D. from the University of Connecticut in 1981. While a doctoral candidate, she was awarded a research assistantship in the Bureau of Educational Research and was named a Young Woman Scholar by the Ford Foundation. She served as Associate Professor teaching research methodology at the graduate and undergraduate levels. Dr. Carroll has written numerous articles published in peer review and trade journals. She has received awards for scholarship, marketing and leadership and has been invited to provide professional development to educators throughout the United States.

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Mathematics: Textbooks (Math and Statistics)

Problems and exercises

Textbooks (Math and Statistics)

Pages in this guide

Finding textbooks.

The Science (Hayden), Barker, and Dewey Libraries hold several mathematics and applied mathematics textbooks.  The lists below show a few titles for some broad and specific subjects.  You should find textbooks on similar subjects when you search for these books in the stacks.

Browse Series Title in the Barton catalog :

Graduate texts in mathematics

Graduate studies in mathematics

Monographs and textbooks in pure and applied mathematics

Undergraduate texts in mathematics

Universitext

Find other textbooks in the Barton catalog with the subject keyword textbooks and a subject keyword such as Measure theory

General mathematics

• A Concise introduction to pure mathematics - Liebeck
• A Course in mathematical logic for mathematicians - Manin Paper and online versions
• Fuzzy logic for beginners - Mukaidono
• An Introrduction to mathematical logic and type theory: to truth through proof - Andrews

Numerical methods

• A First course in numerical methods - Ascher
• Learning Matlab - Driscoll paper and online through Books24x&7

Applied mathematics

• Course in abstract harmonic analysis - Folland
• Wavelets: a primer - Blatter print and online through Books24x7
• Wavelets: mathematics and applications - Bendetto
• First course in wavelets with Fourier analysis - Boggess

Combinatorics and Graph theory

• Graphs and applications: an introductory approach - Aldous
• Path to combinatorics for undergraduates: counting strategies - Andreeescu
• Combinatorics of coxeter groups - Bjorner
• Enumerative combinatorics - Stanley
• Applied combinatorics - Tucker

Group Theory

• Buildings: theory and applications - Abramenko print and online
• Groups and representations - Alperin
• Groups and symmetry - Armstrong
• Matrix groups : an introduction to Lie group theory - Baker
• The Geometry of discrete groups -. Beardon.
• Introduction to the theory of groups - Rotman
• Algebra: An Approach via Module Theory - Adkins
• Complex variables: Introduction and applications
• Introduction to abstract algebra - Nicholson
• Real analysis - Royden
• Introduction to lattices and order - Davey
• Conceptual mathematics: a first introduction to categories - Lawvere
• Introduction to representation theory - Etingof

Global analysis

• Manifolds, Tensor Analysis, and Applications - Abraham

Probability and statistics

• Measure Theory and Probability - Adams
• Measure Theory and Probability Theory - Athreya print and online
• Probability with Statistical Applications - Schinazi
• Probability: theory and examples - Durrett
• Probability theory: an analytic view - Stroock
• An Introduction to probability and stochastic processes - Berger
• Probability and statistical inference - Hogg
• First course in probability - Ross
• Robust statistics - Huber
• Linear statistical models - Stapleton
• Stochastic processes - Ross
• Calculus - Spivak
• Calculus: an introduction to applied mathematics - Greenspan
• Multivariate calculus - Edwards & Penney

Differential equations

• Ordinary differential equations: qualitative Theory - Barreira
• Ordinary differential equations - Hartman print and online through Siam e-books
• Ordinary and partial differential equations with special functions, Fourier series, and boundary value problesm - Agarwal
• Partial differential equations for probabilists - Stroock
• A First course in the numerical analysis of differential equations - Iserles Print and online through Books24x7
• Perturbations: theory and methods - Murdock
• Computer methods for ordinary differential equations and differential-algebraic equations print and online through SIAM e-Books
• Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems - LeVeque print and online through SIAM e-Books
• Fine difference schemes and partial differential equations - Strikwerda print and online through SIAM e-Books
• Partial differential equations: modeling, analysis, computation - Mattheij print and online through SIAM e-Books
• Ordinary differential equations - Arnold
• Differential equations and their applications: an introduction to applied mathematics - Braun
• Understanding analysis - Abbott
• From calculus to analysis - Schinazi
• Complex variables: introduction and applications - Ablowitz
• Applied complex variables for scientists and engineers - Kwok
• A First course in real analysis - Berberian
• Complex variables: an introduction - Berenstein
• Real analysis and probability - Dudley

Algebraic geometry

• Geometry of algebraic curves - Abarello print and online for v. 2 via Springerlink
• Algorithms in real algebraic geometry - Basu print and online through Springerlink
• Conics and cubics: a concrete introduction to algebraic curves - Bix
• Introduction to elliptic curves and modular forms - Koblitz
• Geometry of curves - Rutter

Differential geomety

• Curves and surfaces - Abate
• Differential geometry: curves surfaces manifolds - Kuhnel
• Curves and surfaces - Montiel
• Geometry from a differentiable viewpoint - McCleary
• Differential geometry: manifolds, curves, and surfaces - Berger
• Modern differential geometry of curves and surfaces with Mathematica - Gray
• Elements of differential geometry - Millman
• Plane and Solid Geometry - Aarts
• A General topology workbook - Adamson
• Algebraic topology - Hatcher
• Riemmanian geometry: a beginner's guide - Morgan
• Riemannian geometry: a modern introduction - Chavel
• Differential dynamic systems - Meiss paper and SIAM e-Books
• Basic topology - Armstrong
• Introduction to intesection homology theory - Kirwan
• Essentials of topology with applications - Krantz
• Topology - Munkres
• Elements of algebraic topology - Munkres

Discrete geometry

• Lectures on Discrete Geometry - Matousek

Number theory

• An Introduction to the Theory of Numbers - Hardy
• Introduction to analytic number theory - Apostol
• Introduction to number theory - Erickson

Linear and mulitlinear algebra

• Matrix Analysis - Horn
• Matrix analysis and applied linear algebra - Meyer print and online through SIAM e-Books and Books24x7
• Numerical linear algebra - Trefethen print and online through SIAM e-Books
• Linear algebra done right - Axler
• Introduction to linear algebra - Strang
• Linear algebra and its applications - Strang
• Lienar algebra through geometry - Banchoff

Librarian for Electrical Engineering & Computer Science, IDSS, and Mathematics

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• Last Updated: Apr 19, 2024 8:37 AM
• URL: https://libguides.mit.edu/math

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These are all resources you may find helpful in your first few years (e.g. to supplement the core courses and/or starting research). Unless noted otherwise, they are all freely available online.

Probability, Statistics, Machine Learning and Optimization

Probability Theory and Examples by Rick Durrett ( http://services.math.duke.edu/~rtd/PTE/PTE4_1.pdf ) – One of the preferred grad level probability textbooks.

Jeff Miller has an excellent series of youtube videos – Probability primer ( https://www.youtube.com/playlist?list=PL17567A1A3F5DB5E4 ). This course covers some topics in probability (634-635) and stat theory (654-655). – Machine learning ( https://www.youtube.com/playlist?list=PLD0F06AA0D2E8FFBA) . This course overs many topics in stat theory (654-655) and applied stats (664-665). It also covers topics in machine learning and bayesian stat courses.

Introduction to Statistical Learning ( http://www-bcf.usc.edu/~gareth/ISL/ISLR%20Seventh%20Printing.pdf ) and Elements of Statistical Learning ( https://web.stanford.edu/~hastie/Papers/ESLII.pdf ) – These are great places to turn for your first (and second) foray applied statistics and machine learning.

Michael Jordan’s suggested reading list for statistics PhD:  https://honglangwang.wordpress.com/2014/12/30/machine-learning-books-suggested-by-michael-i-jordan-from-berkeley/  (not free)

The deep learning book ( http://www.deeplearningbook.org/ ) – Introductory/intermediate level textbook form some of the masters. – Also a good book to machine learning and optimization.

Convex Optimization by Vandenberghe and Boyd  ( https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf) – The standard introduction to optimization. – Also see the course webpage ( http://www.seas.ucla.edu/~vandenbe/ee236b/ee236b.html ) and Stephen Boyd’s youtube lectures ( https://www.youtube.com/view_play_list?p=3940DD956CDF0622 )

Optimization Methods for Large-Scale Machine Learning ( https://arxiv.org/pdf/1606.04838.pdf ) – Overview of many of the modern optimization methods that statisticians/machine learning researchers should at least be aware of.

Computation

These are helpful resources for getting started in R/Python and for learning some more advanced topics.

Introductory R

R for Data Science http by Hadley Wickham ( http://r4ds.had.co.nz/ ) – Fantastic, free, online textbook for introductory to intermediate R.

STOR 320: Intro to Data Science ( https://idc9.github.io/stor390/ ) – Undergrad course at UNC which introduces R and data science.

Introductory Python

Python Data Science Handbook by Jake Vanderplas ( https://jakevdp.github.io/PythonDataScienceHandbook/ ) – Introduction to doing statistics/machine learning in Python.

Computational Statistics in Python by Cliburn Chan  ( http://people.duke.edu/~ccc14/sta-663-2017/ ) – Covers a huge number of topics in computational statistics from advanced python to MCMC to GPU computing.

Other Helpful Resources and More Advanced Topics

Computational Linear Algebra by fast.ai ( https://github.com/fastai/numerical-linear-algebra ) – Covers things like PCA, robust PCA, non-negative matrix factorization, large scale linear regression all in Python.

Lot’s of small coding examples in Python/R:  https://chrisalbon.com/

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DEPARTMENT OF STATISTICS AND DATA SCIENCE

Phd program, phd program overview.

The doctoral program in Statistics and Data Science is designed to provide students with comprehensive training in theory and methodology in statistics and data science, and their applications to problems in a wide range of fields. The program is flexible and may be arranged to reflect students' interests and career goals. Cross-disciplinary work is encouraged. The PhD program prepares students for careers as university teachers and researchers and as research statisticians or data scientists in industry, government and the non-profit sector.

Requirements

Students are required to fulfill the Department requirements in addition to those specified by The Graduate School (TGS).

From the Graduate School’s webpage outlining the general requirements for a PhD :

In order to receive a doctoral degree, students must:

• Complete all required coursework. .
• Gain admittance to candidacy.
• Submit a prospectus to be approved by a faculty committee.
• Present a dissertation with original research. Review the Dissertation Publication page for more information.
• Complete the necessary teaching requirement
• Submit necessary forms to file for graduation
• Complete degree requirements within the approved timeline

PhD degrees must be approved by the student's academic program. Consult with your program directly regarding specific degree requirements.

The Department requires that students in the Statistics and Data Science PhD program:

• Meet the department minimum residency requirement of 2 years
• STAT 344-0 Statistical Computing
• STAT 350-0 Regression Analysis
• STAT 353-0 Advanced Regression (new 2021-22)
• STAT 415-0 I ntroduction to Machine Learning
• STAT 420-1,2,3 Introduction to Statistical Theory and Methodology 1, 2, 3
• STAT 430-1, STAT 430-2, STAT 440 (new courses in 2022-23 on probability and stochastic processes for statistics students)
• STAT 457-0 Applied Bayesian Inference

Students generally complete the required coursework during their first two years in the PhD program. *note that required courses changed in the 2021-22 academic year, previous required courses can be found at the end of this page.

• Pass the Qualifying Exam. This comprehensive examination covers basic topics in statistics and is typically taken in fall quarter of the second year.

Pass the Prospectus presentation/examination and be admitted for PhD candidacy by the end of year 3 . The statistics department requires that students must complete their Prospectus (proposal of dissertation topic) before the end of year 3, which is earlier than The Graduate School deadline of the end of year 4. The prospectus must be approved by a faculty committee comprised of a committee chair and a minimum of 2 other faculty members. Students usually first find an adviser through independent studies who will then typically serve as the committee chair. When necessary, exceptions may be made upon the approval of the committee chair and the director of graduate studies, to extend the due date of the prospectus exam until the end of year 4.

• Successfully complete and defend a doctoral dissertation. After the prospectus is approved, students begin work on the doctoral dissertation, which must demonstrate an original contribution to a chosen area of specialization. A final examination (thesis defense) is given based on the dissertation. Students typically complete the PhD program in 5 years.
• Attend all seminars in the department and participate in other research activities . In addition to these academic requirements, students are expected to participate in other research activities and attend all department seminars every year they are in the program.

Optional MS degree en route to PhD

Students admitted to the Statistics and Data Science PhD program can obtain an optional MS (Master of Science) degree en route to their PhD. The MS degree requires 12 courses: STAT 350-0 Regression Analysis, STAT 353 Advanced Regression, STAT 420-1,2,3 Introduction to Statistical Theory and Methodology 1, 2, 3, STAT 415-0 I ntroduction to Machine Learning , and at least 6 more courses approved by the department of which two must be 400 level STAT elective courses, no more than 3 can be non-STAT courses. For the optional MS degree, students must also pass the qualifying exam offered at the beginning of the second year at the MS level.

*Prior to 2021-2022, the course requirements for the PhD were:

• STAT 351-0 Design and Analysis of Experiments
• STAT 425 Sampling Theory and Applications
• MATH 450-1,2 Probability 1, 2 or MATH 450-1 Probability 1 and IEMS 460-1,2 Stochastic Processes 1, 2
• Six additional 300/400 graduate-level Statistics courses, at least two must be 400 -level

• Graduate Studies

Ph.D. Program

The PhD program prepares students for research careers in theory and application of probability and statistics in academic and non-academic (e.g., industry, government) settings.  Students might elect to pursue either the general Statistics track of the program (the default), or one of the four specialized tracks that take advantage of UW’s interdisciplinary environment: Statistical Genetics (StatGen), Statistics in the Social Sciences (CSSS), Machine Learning and Big Data (MLBD), and Advanced Data Science (ADS). 

Admission Requirements

For application requirements and procedures, please see the graduate programs applications page .

Recommended Preparation

The Department of Statistics at the University of Washington is committed to providing a world-class education in statistics. As such, having some mathematical background is necessary to complete our core courses. This background includes linear algebra at the level of UW’s MATH 318 or 340, advanced calculus at the level of MATH 327 and 328, and introductory probability at the level of MATH 394 and 395. Real analysis at the level of UW’s MATH 424, 425, and 426 is also helpful, though not required. Descriptions of these courses can be found in the UW Course Catalog . We also recognize that some exceptional candidates will lack the needed mathematical background but succeed in our program. Admission for such applicants will involve a collaborative curriculum design process with the Graduate Program Coordinator to allow them to make up the necessary courses. 

While not a requirement, prior background in computing and data analysis is advantageous for admission to our program. In particular, programming experience at the level of UW’s CSE 142 is expected.  Additionally, our coursework assumes familiarity with a high-level programming language such as R or Python. 

Graduation Requirements 

This is a summary of the department-specific graduation requirements. For additional details on the department-specific requirements, please consult the  Ph.D. Student Handbook .  For previous versions of the Handbook, please contact the Graduate Student Advisor .  In addition, please see also the University-wide requirements at  Instructions, Policies & Procedures for Graduate Students  and  UW Doctoral Degrees .  

General Statistics Track

• Core courses: Advanced statistical theory (STAT 581, STAT 582 and STAT 583), statistical methodology (STAT 570 and STAT 571), statistical computing (STAT 534), and measure theory (either STAT 559 or MATH 574-575-576).  
• Elective courses: A minimum of four approved 500-level classes that form a coherent set, as approved in writing by the Graduate Program Coordinator.  A list of elective courses that have already been pre-approved or pre-denied can be found here .
• M.S. Theory Exam: The syllabus of the exam is available here .
• Research Prelim Exam. Requires enrollment in STAT 572. 
• Consulting.  Requires enrollment in STAT 599. 
• Applied Data Analysis Project.  Requires enrollment in 3 credits of STAT 597. 
• Statistics seminar participation: Students must attend the Statistics Department seminar and enroll in STAT 590 for at least 8 quarters. 
• Teaching requirement: All Ph.D. students must satisfactorily serve as a Teaching Assistant for at least one quarter. 
• General Exam. 
• Dissertation Credits.  A minimum of 27 credits of STAT 800, spread over at least three quarters. 
• Passage of the Dissertation Defense. 

Statistical Genetics (StatGen) Track

Students pursuing the Statistical Genetics (StatGen) Ph.D. track are required to take BIOST/STAT 550 and BIOST/STAT 551, GENOME 562 and GENOME 540 or GENOME 541. These courses may be counted as the four required Ph.D.-level electives. Additionally, students are expected to participate in the Statistical Genetics Seminar (BIOST581) in addition to participating in the statistics seminar (STAT 590). Finally, students in the Statistics Statistical Genetics Ph.D. pathway may take STAT 516-517 instead of STAT 570-571 for their Statistical Methodology core requirement. This is a transcriptable program option, i.e., the fact that the student completed the requirements will be noted in their transcript.

Statistics in the Social Sciences (CSSS) Track

Students in the Statistics in the Social Sciences (CSSS) Ph.D. track  are required to take four numerically graded 500-level courses, including at least two CSSS courses or STAT courses cross-listed with CSSS, and at most two discipline-specific social science courses that together form a coherent program of study. Additionally, students must complete at least three quarters of participation (one credit per quarter) in the CS&SS seminar (CSSS 590). This is not a transcriptable option, i.e., the fact that the student completed the requirements will not be noted in their transcript.

Machine Learning and Big Data Track

Students in the Machine Learning and Big Data (MLBD) Ph.D. track are required to take the following courses: one foundational machine learning course (STAT 535), one advanced machine learning course (either STAT 538 or STAT 548 / CSE 547), one breadth course (either on databases, CSE 544, or data visualization, CSE 512), and one additional elective course (STAT 538, STAT 548, CSE 515, CSE 512, CSE 544 or EE 578). At most two of these four courses may be counted as part of the four required PhD-level electives. Students pursuing this track are not required to take STAT 583 and can use STAT 571 to satisfy the Applied Data Analysis Project requirement. This is not a transcriptable option, i.e., the fact that the student completed the requirements will not be noted in their transcript. 

Advanced Data Science (ADS) Track

Students in the Advanced Data Science (ADS) Ph.D. track are required to take the same coursework as students in the Machine Learning and Big Data track. They are also not required to take STAT 583 and can use STAT 571 to satisfy the Applied Data Analysis Project requirement. The only difference in terms of requirements between the MLBD and the ADS tracks is that students in the ADS track must also register for at least 4 quarters of the weekly eScience Community Seminar (CHEM E 599). Also, unlike the MLBD track, the ADS is a transcriptable program option, i.e., the fact that the student completed the requirements will be noted in their transcript. 

PhD Program information

The Statistics PhD program is rigorous, yet welcoming to students with interdisciplinary interests and different levels of preparation. Students in the PhD program take core courses on the theory and application of probability and statistics during their first year. The second year typically includes additional course work and a transition to research leading to a dissertation. PhD thesis topics are diverse and varied, reflecting the scope of faculty research interests. Many students are involved in interdisciplinary research. Students may also have the option to pursue a designated emphasis (DE) which is an interdisciplinary specialization:  Designated Emphasis in Computational and Genomic Biology ,  Designated Emphasis in Computational Precision Health ,  Designated Emphasis in Computational and Data Science and Engineering . The program requires four semesters of residence.

Normal progress entails:

Year 1 . Perform satisfactorily in preliminary coursework. In the summer, students are required to embark on a short-term research project, internship, graduate student instructorship, reading course, or on another research activity. Years 2-3 . Continue coursework. Find a thesis advisor and an area for the oral qualifying exam. Formally choose a chair for qualifying exam committee, who will also serve as faculty mentor separate from the thesis advisor.  Pass the oral qualifying exam and advance to candidacy by the end of Year 3. Present research at BSTARS each year. Years 4-5 . Finish the thesis and give a lecture based on it in a department seminar.

Program Requirements

• Qualifying Exam

Course work and evaluation

Preliminary stage: the first year.

Effective Fall 2019, students are expected to take four semester-long courses for a letter grade during their first year which should be selected from the core first-year PhD courses offered in the department: Probability (204/205A, 205B,), Theoretical Statistics (210A, 210B), and Applied Statistics (215A, 215B). These requirements can be altered by a member of the PhD Program Committee (in consultation with the faculty mentor and by submitting a graduate student petition ) in the following cases:

• Students primarily focused on probability will be allowed to substitute one semester of the four required semester-long courses with an appropriate course from outside the department.
• Students may request to postpone one semester of the core PhD courses and complete it in the second year, in which case they must take a relevant graduate course in their first year in its place. In all cases, students must complete the first year requirements in their second year as well as maintain the overall expectations of second year coursework, described below. Some examples in which such a request might be approved are described in the course guidance below.
• Students arriving with advanced standing, having completed equivalent coursework at another institution prior to joining the program, may be allowed to take other relevant graduate courses at UC Berkeley to satisfy some or all of the first year requirements

Requirements on course work beyond the first year

Students entering the program before 2022 are required to take five additional graduate courses beyond the four required in the first year, resulting in a total of nine graduate courses required for completion of their PhD. In their second year, students are required to take three graduate courses, at least two of them from the department offerings, and in their third year, they are required to take at least two graduate courses. Students are allowed to change the timing of these five courses with approval of their faculty mentor. Of the nine required graduate courses, students are required to take for credit a total of 24 semester hours of courses offered by the Statistics department numbered 204-272 inclusive. The Head Graduate Advisor (in consultation with the faculty mentor and after submission of a graduate student petition) may consent to substitute courses at a comparable level in other disciplines for some of these departmental graduate courses. In addition, the HGA may waive part of this unit requirement.

Starting with the cohort entering in the 2022-23 academic year , students are required to take at least three additional graduate courses beyond the four required in the first year, resulting in a total of seven graduate courses required for completion of their PhD. Of the seven required graduate courses, five of these courses must be from courses offered by the Statistics department and numbered 204-272, inclusive. With these reduced requirements, there is an expectation of very few waivers from the HGA. We emphasize that these are minimum requirements, and we expect that students will take additional classes of interest, for example on a S/U basis, to further their breadth of knowledge. 

For courses to count toward the coursework requirements students must receive at least a B+ in the course (courses taken S/U do not count, except for STAT 272 which is only offered S/U).  Courses that are research credits, directed study, reading groups, or departmental seminars do not satisfy coursework requirements (for courses offered by the Statistics department the course should be numbered 204-272 to satisfy the requirements). Upper-division undergraduate courses in other departments can be counted toward course requirements with the permission of the Head Graduate Advisor. This will normally only be approved if the courses provide necessary breadth in an application area relevant to the student’s thesis research.

First year course work: For the purposes of satisfactory progression in the first year, grades in the core PhD courses are evaluated as: A+: Excellent performance in PhD program A: Good performance in PhD program A-: Satisfactory performance B+: Performance marginal, needs improvement B: Unsatisfactory performance First year and beyond: At the end of each year, students must meet with his or her faculty mentor to review their progress and assess whether the student is meeting expected milestones. The result of this meeting should be the completion of the student’s annual review form, signed by the mentor ( available here ). If the student has a thesis advisor, the thesis advisor must also sign the annual review form.

Guidance on choosing course work

Choice of courses in the first year: Students enrolling in the fall of 2019 or later are required to take four semesters of the core PhD courses, at least three of which must be taken in their first year. Students have two options for how to schedule their four core courses:

• Option 1 -- Complete Four Core Courses in 1st year: In this option, students would take four core courses in the first year, usually finishing the complete sequence of two of the three sequences.  Students following this option who are primarily interested in statistics would normally take the 210A,B sequence (Theoretical Statistics) and then one of the 205A,B sequence (Probability) or the 215A,B sequence (Applied Statistics), based on their interests, though students are allowed to mix and match, where feasible. Students who opt for taking the full 210AB sequence in the first year should be aware that 210B requires some graduate-level probability concepts that are normally introduced in 205A (or 204).
• Option 2 -- Postponement of one semester of a core course to the second year: In this option, students would take three of the core courses in the first year plus another graduate course, and take the remaining core course in their second year. An example would be a student who wanted to take courses in each of the three sequences. Such a student could take the full year of one sequence and the first semester of another sequence in the first year, and the first semester of the last sequence in the second year (e.g. 210A, 215AB in the first year, and then 204 or 205A in the second year). This would also be a good option for students who would prefer to take 210A and 215A in their first semester but are concerned about their preparation for 210B in the spring semester.  Similarly, a student with strong interests in another discipline, might postpone one of the spring core PhD courses to the second year in order to take a course in that discipline in the first year.  Students who are less mathematically prepared might also be allowed to take the upper division (under-graduate) courses Math 104 and/or 105 in their first year in preparation for 205A and/or 210B in their second year. Students who wish to take this option should consult with their faculty mentor, and then must submit a graduate student petition to the PhD Committee to request permission for  postponement. Such postponement requests will be generally approved for only one course. At all times, students must take four approved graduate courses for a letter grade in their first year.

After the first year: Students with interests primarily in statistics are expected to take at least one semester of each of the core PhD sequences during their studies. Therefore at least one semester (if not both semesters) of the remaining core sequence would normally be completed during the second year. The remaining curriculum for the second and third years would be filled out with further graduate courses in Statistics and with courses from other departments. Students are expected to acquire some experience and proficiency in computing. Students are also expected to attend at least one departmental seminar per week. The precise program of study will be decided in consultation with the student’s faculty mentor.

Remark. Stat 204 is a graduate level probability course that is an alternative to 205AB series that covers probability concepts most commonly found in the applications of probability. It is not taught all years, but does fulfill the requirements of the first year core PhD courses. Students taking Stat 204, who wish to continue in Stat 205B, can do so (after obtaining the approval of the 205B instructor), by taking an intensive one month reading course over winter break.

Designated Emphasis: Students with a Designated Emphasis in Computational and Genomic Biology or Designated Emphasis in Computational and Data Science and Engineering should, like other statistics students, acquire a firm foundation in statistics and probability, with a program of study similar to those above. These programs have additional requirements as well. Interested students should consult with the graduate advisor of these programs. 

Starting in the Fall of 2019, PhD students are required in their first year to take four semesters of the core PhD courses. Students intending to specialize in Probability, however, have the option to substitute an advanced mathematics class for one of these four courses. Such students will thus be required to take Stat 205A/B in the first year,  at least one of Stat 210A/B or Stat 215A/B in the first year, in addition to an advanced mathematics course. This substitute course will be selected in consultation with their faculty mentor, with some possible courses suggested below. Students arriving with advanced coursework equivalent to that of 205AB can obtain permission to substitute in other advanced probability and mathematics coursework during their first year, and should consult with the PhD committee for such a waiver.

During their second and third years, students with a probability focus are expected to take advanced probability courses (e.g., Stat 206 and Stat 260) to fulfill the coursework requirements that follow the first year. Students are also expected to attend at least one departmental seminar per week, usually the probability seminar. If they are not sufficiently familiar with measure theory and functional analysis, then they should take one or both of Math 202A and Math 202B. Other recommended courses from the department of Mathematics or EECS include:

Math 204, 222 (ODE, PDE) Math 205 (Complex Analysis) Math 258 (Classical harmonic analysis) EE 229 (Information Theory and Coding) CS 271 (Randomness and computation)

The Qualifying Examination 

The oral qualifying examination is meant to determine whether the student is ready to enter the research phase of graduate studies. It consists of a 50-minute lecture by the student on a topic selected jointly by the student and the thesis advisor. The examination committee consists of at least four faculty members to be approved by the department.  At least two members of the committee must consist of faculty from the Statistics and must be members of the Academic Senate. The chair must be a member of the student’s degree-granting program.

Qualifying Exam Chair. For qualifying exam committees formed in the Fall of 2019 or later, the qualifying exam chair will also serve as the student’s departmental mentor, unless a student already has two thesis advisors. The student must select a qualifying exam chair and obtain their agreement to serve as their qualifying exam chair and faculty mentor. The student's prospective thesis advisor cannot chair the examination committee. Selection of the chair can be done well in advance of the qualifying exam and the rest of the qualifying committee, and because the qualifying exam chair also serves as the student’s departmental mentor (unless the student has co-advisors), the chair is expected to be selected by the beginning of the third year or at the beginning of the semester of the qualifying exam, whichever comes earlier. For more details regarding the selection of the Qualifying Exam Chair, see the "Mentoring" tab.  

Paperwork and Application. Students at the point of taking a qualifying exam are assumed to have already found a thesis advisor and to should have already submitted the internal departmental form to the Graduate Student Services Advisor ( found here ).  Selection of a qualifying exam chair requires that the faculty member formally agree by signing the internal department form ( found here ) and the student must submit this form to the Graduate Student Services Advisor.  In order to apply to take the exam, the student must submit the Application for the Qualifying Exam via CalCentral at least three weeks prior to the exam. If the student passes the exam, they can then officially advance to candidacy for the Ph.D. If the student fails the exam, the committee may vote to allow a second attempt. Regulations of the Graduate Division permit at most two attempts to pass the oral qualifying exam. After passing the exam, the student must submit the Application for Candidacy via CalCentral .

The Doctoral Thesis

The Ph.D. degree is granted upon completion of an original thesis acceptable to a committee of at least three faculty members. The majority or at least half of the committee must consist of faculty from Statistics and must be members of the Academic Senate. The thesis should be presented at an appropriate seminar in the department prior to filing with the Dean of the Graduate Division. See Alumni if you would like to view thesis titles of former PhD Students.

Graduate Division offers various resources, including a workshop, on how to write a thesis, from beginning to end. Requirements for the format of the thesis are rather strict. For workshop dates and guidelines for submitting a dissertation, visit the Graduate Division website.

Students who have advanced from candidacy (i.e. have taken their qualifying exam and submitted the advancement to candidacy application) must have a joint meeting with their QE chair and their PhD advisor to discuss their thesis progression; if students are co-advised, this should be a joint meeting with their co-advisors. This annual review is required by Graduate Division.  For more information regarding this requirement, please see  https://grad.berkeley.edu/ policy/degrees-policy/#f35- annual-review-of-doctoral- candidates .

Teaching Requirement

For students enrolled in the graduate program before Fall 2016, students are required to serve as a Graduate Student Instructor (GSI) for a minimum of 20 hours (equivalent to a 50% GSI appointment) during a regular academic semester by the end of their third year in the program.

Effective with the Fall 2016 entering class, students are required to serve as a GSI for a minimum of two 50% GSI appointment during the regular academic semesters prior to graduation (20 hours a week is equivalent to a 50% GSI appointment for a semester) for Statistics courses numbered 150 and above. Exceptions to this policy are routinely made by the department.

Each spring, the department hosts an annual conference called BSTARS . Both students and industry alliance partners present research in the form of posters and lightning talks. All students in their second year and beyond are required to present a poster at BSTARS each year. This requirement is intended to acclimate students to presenting their research and allow the department generally to see the fruits of their research. It is also an opportunity for less advanced students to see examples of research of more senior students. However, any students who do not yet have research to present can be exempted at the request of their thesis advisor (or their faculty mentors if an advisor has not yet been determined).

Mentoring for PhD Students

Initial Mentoring: PhD students will be assigned a faculty mentor in the summer before their first year. This faculty mentor at this stage is not expected to be the student’s PhD advisor nor even have research interests that closely align with the student. The job of this faculty mentor is primarily to advise the student on how to find a thesis advisor and in selecting appropriate courses, as well as other degree-related topics such as applying for fellowships.  Students should meet with their faculty mentors twice a semester. This faculty member will be the designated faculty mentor for the student during roughly their first two years, at which point students will find a qualifying exam chair who will take over the role of mentoring the student.

Research-focused mentoring : Once students have found a thesis advisor, that person will naturally be the faculty member most directly overseeing the student’s progression. However, students will also choose an additional faculty member to serve as a the chair of their qualifying exam and who will also serve as a faculty mentor for the student and as a member of his/her thesis committee. (For students who have two thesis advisors, however, there is not an additional faculty mentor, and the quals chair does NOT serve as the faculty mentor).

The student will be responsible for identifying and asking a faculty member to be the chair of his/her quals committee. Students should determine their qualifying exam chair either at the beginning of the semester of the qualifying exam or in the fall semester of the third year, whichever is earlier. Students are expected to have narrowed in on a thesis advisor and research topic by the fall semester of their third year (and may have already taken qualifying exams), but in the case where this has not happened, such students should find a quals chair as soon as feasible afterward to serve as faculty mentor.

Students are required to meet with their QE chair once a semester during the academic year. In the fall, this meeting will generally be just a meeting with the student and the QE chair, but in the spring it must be a joint meeting with the student, the QE chair, and the PhD advisor. If students are co-advised, this should be a joint meeting with their co-advisors.

If there is a need for a substitute faculty mentor (e.g. existing faculty mentor is on sabbatical or there has been a significant shift in research direction), the student should bring this to the attention of the PhD Committee for assistance.

PhD Student Forms:

Important milestones: .

Each of these milestones is not complete until you have filled out the requisite form and submitted it to the GSAO. If you are not meeting these milestones by the below deadline, you need to meet with the Head Graduate Advisor to ask for an extension. Otherwise, you will be in danger of not being in good academic standing and being ineligible for continued funding (including GSI or GSR appointments, and many fellowships). 

†Students who are considering a co-advisor, should have at least one advisor formally identified by the end of the second year; the co-advisor should be identified by the end of the fall semester of the 3rd year in lieu of finding a Research Mentor/QE Chair.

Expected Progress Reviews: 

* These meetings do not need to be held in the semester that you take your Qualifying Exam, since the relevant people should be members of your exam committee and will discuss your research progress during your qualifying exam

** If you are being co-advised by someone who is not your primary advisor because your primary advisor cannot be your sole advisor, you should be meeting with that person like a research mentor, if not more frequently, to keep them apprised of your progress. However, if both of your co-advisors are leading your research (perhaps independently) and meeting with you frequently throughout the semester, you do not need to give a fall research progress report.

PhD in Statistics

Program description.

The Ph.D. program in statistics prepares students for a career pursuing research in either academia or industry.  The program provides rigorous classroom training in the theory, methodology, and application of statistics, and provides the opportunity to work with faculty on advanced research topics over a wide range of theory and application areas. To enter, students need a bachelor’s degree in mathematics, statistics, or a closely related discipline. Students graduating with a PhD in Statistics are expected to:

• Demonstrate an understanding the core principles of Probability Theory, Estimation Theory, and Statistical Methods.
• Demonstrate the ability to conduct original research in statistics.
• Demonstrate the ability to present research-level statistics in a formal lecture

Requirements for the Ph.D. (Statistics Track)

Course Work A Ph.D. student in our department must complete sixteen courses for the Ph.D. At most, four of these courses may be transferred from another institution. If the Ph.D. student is admitted to the program at the post-Master’s level, then eight courses are usually required.

Qualifying Examinations First, all Ph.D. students in the statistics track must take the following two-semester sequences: MA779 and MA780 (Probability Theory I and II), MA781 (Estimation Theory) and MA782 (Hypothesis Testing), and MA750 and MA751 (Advanced Statistical Methods I and II). Then, to qualify a student to begin work on a PhD dissertation, they must pass two of the following three exams at the PhD level: probability, mathematical statistics, and applied statistics. The probability and mathematical statistics exams are offered every September and the applied statistics exam is offered every April.

• PhD Exam in Probability: This exam covers the material covered in MA779 and MA780 (Probability Theory I and II).
• PhD Exam in Mathematical Statistics: This exam covers material covered in MA781 (Estimation Theory) and MA782 (Hypothesis Testing).
• PhD Exam in Applied Statistics: This exam covers the same material as the M.A. Applied exam and is offered at the same time, except that in order to pass it at the PhD level a student must correctly solve all four problems.

Note: Students concentrating in probability may choose to do so either through the statistics track or through the mathematics track. If a student wishes to do so through the mathematics track, the course and exam requirements are different. Details are available here .

Dissertation The dissertation is the major requirement for a Ph.D. student. After the student has completed all course work, the Director of Graduate Studies, in consultation with the student, selects a three-member dissertation committee. One member of this committee is designated by the Director of Graduate Studies as the Major Advisor for the student. Once completed, the dissertation must be defended in an oral examination conducted by at least five members of the Department.

The Dissertation and Final Oral Examination follows the   GRS General Requirements for the Doctor of Philosophy Degree .

Satisfactory Progress Toward the Degree Upon entering the graduate program, each student should consult the Director of Graduate Studies (Prof. David Rohrlich) and the Associate Director of the Program in Statistics (Prof. Konstantinos Spiliopoulos). Initially, the Associate Director of the Program in Statistics will serve as the default advisor to the student. Eventually the student’s advisor will be determined in conjunction with their dissertation research. The Associate Director of the Program in Statistics, who will be able to guide the student through the course selection and possible directed study, should be consulted often, as should the Director of Graduate Studies. Indeed, the Department considers it important that each student progress in a timely manner toward the degree. Each M.A. student must have completed the examination by the end of their second year in the program, while a Ph.D. student must have completed the qualifying examination by the third year. Students entering the Ph.D. program with an M.A. degree must have completed the qualifying examination by October of the second year. Failure to meet these deadlines may jeopardize financial aid. Some flexibility in the deadlines is possible upon petition to the graduate committee in cases of inadequate preparation.

Students enrolled in the Graduate School of Arts & Sciences (GRS) are expected to adhere to a number of policies at the university, college, and departmental levels. View the policies on the Academic Bulletin and GRS website .

Residency Post-BA students must complete all of the requirements for a Ph.D. within seven years of enrolling in the program and post-MA students must complete all requirements within five years. This total time limit is set by the Graduate School. Students needing extra time must petition the Graduate School. Also, financial aid is not guaranteed after the student’s fifth year in the program.

Financial Aid

As with all Ph.D. students in the Department of Mathematics and Statistics, the main source of financial aid for graduate students studying statistics is a Teaching Fellowship. These awards carry a stipend as well as tuition remission for six courses per year. Teaching Fellows are required to assist a faculty member who is teaching a course, usually a large lecture section of an introductory statistics course. Generally, the Teaching Fellow is responsible for conducting a number of discussion sections consisting of approximately twenty-five students each, as well as for holding office hours and assisting with grading. The Teaching Fellowship usually entails about twenty hours of work per week. For that reason, Teaching Fellows enroll in at most three courses per semester. A Teaching Fellow Seminar is conducted to help new Teaching Fellows develop as instructors and to promote the continuing development of experienced Teaching Fellows.

Other sources of financial aid include University Fellowships and Research Assistantships. The University Fellowships are one-year awards for outstanding students and are service-free. They carry stipends plus full tuition remission. Students do not need to apply for these fellowships. Research Assistantships are linked to research done with individual faculty, and are paid for through those faculty members’ grants. As a result, except on rare occasions, Research Assistantships typically are awarded to students in their second year and beyond, after student and faculty have had sufficient time to determine mutuality of their research interests.

Regular reviews of the performance of Teaching Fellows and Research Assistants in their duties as well as their course work are conducted by members of the Department’s Graduate Committee.

Ph.D. Program Milestones

The department considers it essential that each student progress in a timely manner toward completion of the degree. The following are the deadlines for achieving the milestones described in the Degree Requirements and constitute the basis for evaluating satisfactory progress towards the Ph.D. These deadlines are not to be construed as expected times to complete the various milestones, but rather as upper bounds. In other words,   a student in good standing expecting to complete   the degree within the five years of guaranteed funding will meet these milestones by the much e arlier target dates indicated below.   Failure to achieve these milestones in a timely manner may affectfinancial aid.

• Target: April of Year 1
• Deadline: April of Year 2
• Target: Spring of Year 2 post-BA/Spring of Year 1 post-MA
• Deadline: End of Year 3 post-BA/Fall of Year 2 post-MA
• Target: Spring of Year 2
• Deadline: End of Year 3
• Target: Spring of Year 2 or Fall of Year 3 post-BA/October of Year 2 post-MA
• Deadline: End of Year 3 post-BA/October of Year 2 post-MA
• Target: end of Year 3
• Deadline: End of Year 4
• Target: End of Year 5
• Deadline: End of Year 6

If you have any questions regarding our PhD program in Statistics, please reach out to us at [email protected]

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Statistics PhD Student Handbook

The contents in this handbook are for students in the Statistics-PhD program to navigate the various resources and policies of the doctoral program. Information provided in this guide is relevant as of the posted modify date below. Questions regarding particular processes or policies should be directed at the indicated contacts under each category.

The Statistics-PhD program requires a minimum of 96 credit hours for completion. This is comprised of 64 credit hours at the advanced doctoral level and 32 credit hours at the MS level.

Review complete course requirements here: https://stat.illinois.edu/academics/graduate-programs/phd-statistics/coursework

• Successful completion of the Qualifying Exam will allow a student to continue on to PhD candidacy and allow a student to begin working with research faculty.
• Successfully pass a Preliminary Exam for thesis proposal.
• Successfully pass a Final Exam for thesis proposal.
• Successfully deposit thesis for review.
• Minimum GPA: 3.0
• Students should register for at minimum 0 credit hours of STAT 599 Thesis Research before deposit.

Minimum Grades and Credit for Repeated Courses

The Graduate College has no minimum grade policy, but a department or program may set a minimum grade to be earned in order for a course to count as credit toward the degree. Students are responsible for knowing their departmental requirements.

Students must earn a grade of C- or higher in a course or CR (Credit/No-Credit) in order for the course to be counted towards degree requirements. 

A student can repeat a course that they got a less than favorable grade in, however the original grade will not be replaced and both grades and total hours will count towards the cumulative GPA, as well as appear on the student’s transcripts. Neither the Graduate College or the department allow for graduate level course grades to be replaced. 

Credit/No-Credit (Pass/Fail)

Credit-no credit is a permanent notation on the academic record that may be requested by a student with the adviser’s approval. Students on limited status admission or probation are not allowed to register for credit-no credit course work until the limited status or probation has been removed.

Credit/no credit courses are not counted toward the GPA, but are included as part of the total credit hours and are assessed as credit hours when completing degree audits for graduation. In any one semester, a student may take no more than 4 semester hours on a credit-no credit basis. Over the entire degree program, a student must earn at least 2 hours of graded (A-D) course work for each hour of credit-no credit course work.

A student may amend a credit-no credit request and return to a regular grade mode by filing a second credit-no-credit form and submitting it by the published deadline as indicated in the Graduate College Academic Calendar. Additional information about credit-no credit can be found in the Student Code.

Students may not take the Credit/No-Credit option for any required degree program course.

The following courses will not be approved for Credit/No-Credit:

• STAT 527 (Qualifying Exam Course)
• STAT 528 (Qualifying Exam Course)
• STAT 511 (Qualifying Exam Course)
• STAT 575 (Qualifying Exam Course)
• STAT 553 (PhD Theory Course)
• Either STAT 525 or STAT 542 if used to meet the Computing-related course requirement
• Either STAT 427, STAT 593, or STAT 595 is used to meet the Practicum course requirement
• Either STAT 556, STAT 555, STAT 533, STAT 554, or STAT 576 if used to meet the Stochastic Processes and Time Series course requirement

Elective courses used to satisfy degree requirements may use the Credit/No-Credit option. Only those courses receiving the Credit (CR) notation will be eligible for degree consideration. Courses listed as options to meet one or more core requirements may elect to use Credit/No-Credit only in the event said course is selected as an elective (e.g., STAT 525 may be used to meet the Computing-related course requirement by receiving a standard letter grade, thus STAT 542 can then be selected as Credit/No-Credit in a future term as the Computing-related course requirement will have been met with STAT 525). 

Course registration questions can be addressed here: s [email protected]

Course registration FAQ (Seat Availability, Registration Errors, Course Capacities, Individual Studies & Thesis Research, Internship, etc.): https://stat.illinois.edu/course-information-pages/registration-frequently-asked-questions-info

Registration Errors: https://stat.illinois.edu/course-information-pages/common-registration-errors

Term Specific Registration Information: https://stat.illinois.edu/academics/registration

GRADUATE COLLEGE TIME REQUIREMENTS FOR DEGREE

• Bachelors to PhD Program Time Limits - 7 years from first term enrolled in doctoral program.
• PhD Program Time Limits with a MS at Illinois - 5 years (2 yrs. for MS and 5 yrs. for PhD)
• PhD Program Time Limits with a Non-Illinois MS - 6 years from first term enrolled in doctoral program
• STAT 527 - Advanced Regression Analysis I (4 hours)
• STAT 528 - Advanced Regression Analysis II (4 hours) 
• STAT 511 - Advanced Mathematical Statistics (4 hours)
• STAT 575 - Large sample theory (4 hours)
• Grad Academy is for students entering the PhD program who are already teaching eligible.
• Grad Symposium is for for students entering the PhD program who are not teaching eligible. 
• Complete EPI (International student only)
• Two day exam, four hours each, consisting of five questions per day

Second Year

• Begin work with Research Advisor

Third – Fifth Year

• Prelim Exam (Thesis Proposal)

Fifth – Seventh Year

• Final Exam (Thesis Defense)
• Dissertation Deposit

Annual Reviews

• Annual academic reviews completed in first half of fall term
• Bi-annual TA reviews completed at end of each fall/spring term. ​​​​​​​

The Department of Statistics offers Doctoral students an “Open Offer”, which means they will hold either a teaching or research assistantship or a fellowship for up to five academic years (Fall and Spring terms only) from their first term of enrollment, providing satisfactory progress is evident by the student. After the fifth year if additional thesis work is required, additional support may be provided on a term-by-term basis. Summer support is not guaranteed and is not included in this policy. Students are required to meet the following criteria in order to maintain their “Open Offer” status:

• Secure a thesis advisor by the end of the first academic year.
• Complete any required ESL courses by the end of the first academic year (for international students only) .
• Pass the Qualifying Exam by the end of the first year or pass the make-up exam within one academic year if the first attempt results in a failing grade.
• Not take a leave of absence from the program unless otherwise approved.
• Maintain a satisfactory GPA.
• Not be on probation status at any time during the duration of the program.
• Maintain consistent and regular meetings with thesis advisor.
• Complete the Graduate Student Self-Evaluation by the deadline.
• Complete the Teaching Assistant Self-Evaluation by the deadline.
• Have a satisfactory progress on the Graduate Student Annual Evaluation at all times.

Graduate students who are awarded a research or teaching assistantship must complete the required paperwork each semester to finalize their appointment prior to the appointment start date – August 16 for fall term and January 1 for spring term. Failure to complete this process by the specified dates each semester will delay students’ appointment start date as well as the first paycheck. Start dates cannot and will not be backdated based on a delayed response.

Most students entering the PhD program will need to provide work authorization documentation and complete new hire procedures before their appointments can officially begin. The Statistics Human Resources office will send information on these required documents and procedures before the appointment begins.

Students offered a graduate assistantship assignment are required to reply to the offer letter sent to them before the indicated deadline in order for their appointment to be successfully applied and initiated.

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You are encouraged to apply to multiple funding sources. It would be wrong to claim reimbursement from two sources for the same expense. So when you apply for travel funding, you are implicitly promising that any funds you receive will be used for the purpose for which they were approved, and that you will not be reimbursed from any other source for the covered expenses.

DEPARTMENT OF STATISTICS

Travel funding from the department is restricted to students giving talks or presenting a poster on their work. Summer schools and intensive workshops at national institutes generally qualify for funding also, please check with the Statistic’s Business Office prior to attending. Students are required to request support from their advisor.

Amount of funding:  $2,500 per Academic Year.

Eligibility requirements:  You must be a current PhD student in good standing in the Department of Statistics.

Application procedure:  Complete a pre-approval request through ChromeRiver. (You may need to request access to ChromeRiver. Step 1: Complete the Information Security Compliance Form . Step 2: Email [email protected] asking for access to ChromeRiver, stating you have already completed the Compliance Form.) 

Application deadline:  Apply as early as possible  before  your trip, but no less than 90 days before your trip. Retroactive applications will not be considered.

While planning your trip: Check with Business Office on rules and regulations of purchasing travel expenses (see below for some of the rules).

After funding is approved:  Please check with the Business Office about procedures for paying directly for transportation and conference registration, getting receipts, and claiming for accommodation and other expenses.

After the trip:  complete the  reimbursement form  and email  it with your receipts to the Statistics Business Office ( [email protected] ). Receipts must be original itemized receipts in order to be accepted. Receipts for airfare and lodging must be fully itemized 

Travel Reimbursement Rules & Regulations:

• Travel must serve the best interest of the University of the Illinois System, have a legitimate business purpose, and be related to the employee's job duties. 
• All travel must be by the most direct route, using the most economical mode of transportation available considering travel time, costs, and work requirements. When reserving lodging, employees must request the lowest available rate that does not exceed state lodging maximums.
• Employees should not pay out of pocket for other employees travel expenses
• All receipts must be turned in prior to the 60-days of the conference. If the reimbursement is not submitted prior to 60-day, the employee will be taxed on the reimbursement.
• NOTE: DO NOT VENMO/PAYPAL/etc expenses of the room to each other, as the University will not reimburse the VENMO/PAYPAL/etc.

GRADUATE COLLEGE CONFERENCE TRAVEL AWARD

See the  Graduate College website  for application guidelines. To be considered, complete the  application form  by one week ahead of the Graduate College deadline. Write "Graduate College Conference Travel Award" in the comments box on the application form.

Please see the Graduate College Benefits Grad Map for up to date details on graduate student benefits such as health insurance.

Teaching Assistantship Terms

A.            Evaluations

Students who hold a teaching assistantship with the Department of Statistics are subject to performance evaluations at the end of each academic term the student holds the teaching assistantship. Evaluations are on performance of required duties in conjunction with the assignment of the teaching assistantship.

                1.            Evaluations will be administered at the end of the current academic term that the graduate employee holds the assistantship.

                2.            The graduate employee will be asked to complete a self-evaluation of their performance during the academic term that the appointment was held.

                3.            The graduate employee’s supervisor will at the same time complete a performance evaluation based on the assigned duties during the academic term. The graduate employee will have a chance to review and reply accordingly to the supervisor’s evaluation.

                4.            The Program Director of the graduate employee’s degree program will initiate any further discussion regarding the outcome of the performance evaluation. These discussions can vary based on the evaluation. The Program Director will be forthcoming with the topic of discussion in the event the graduate employee would like to request the presence of a Union Representative from the Graduate Employee Organization.

B.            Responsibilities

Students who hold a teaching assistantship are expected to honor their commitments to the accepted position by satisfactorily completing assigned duties, having clear and responsive communication to the supervisor, and being readily available to begin their assignment effective the start date of their offered position.

                1.            Assistantantship responsibilities may include one or more of the following:

• Involved with instruction
• Teach classes
• Lead lab/discussion groups for a course
• Develop instructional materials
• Proctor exams
• Hold office hours
• Other duties as assigned

C.            Approved/Unapproved Time Off

Graduate employees who hold a teaching assistantship must seek prior approval from their current or next immediate supervisor for any time off during the assigned assistantship period(s) for approved time off (the exception being unforeseen emergencies). In the event the graduate employee has planned holiday or personal time that overlaps from one appointment to another, the employee will need to seek approval from both supervisors.

Assistants shall receive holidays off without loss of pay in accordance with the campus holiday schedule provided by Illinois Human Resources, which may be modified from time to time. Any other event (extended holidays, personal time, or during academic breaks such as spring break, winter break, etc.) which may prevent a graduate assistant from performing their duties effectively during any duration of time outside of the campus designated holidays must be discussed with and approved by the immediate supervisor(s).

D.            Appointment Start Dates

Appointment start dates for the respective terms will always begin on August 16 for fall, January 1 for spring, May 16 or June 16 for summer. Dates outside of those designated days will be determined on a case-by-case basis in the event a graduate employee is unable to begin their appointment on the standard effective date without prior approval otherwise.

If the graduate employee is unable to begin the assigned appointment by the effective date of the received offer and the assigned supervisor does not approve of the requested time, Department HR will modify the offer effective start date to reflect that of the new start date, thus imposing a financial penalty to the first monthly stipend payment.  A base rate calculation of the amount of working days missed in that current pay period will be deducted from the beginning of the pay period to reflect that of the accurate starting date of the graduate employee.

Graduate employees who have a teaching assistantship during the fall and or spring term should seek prior approval from their supervisor(s) before scheduling trips during extended academic breaks, such as winter break.

E.            Resignation/Release

If a graduate assistant wishes to resign after acceptance of an appointment, the assistant must provide a written statement a minimum of fourteen (14) calendar days prior to the effective date of resignation requesting the resignation.

If a graduate assistant wishes to resign from their appointment after the start of the effective date, the employee must schedule a meeting with their supervisor to discuss the resignation and upon a continuation of the request must submit a letter of resignation to the Department HR office. A fourteen (14) calendar day notice is required of resignation.

F.            Procedure for Unsatisfactory Performance or Violation of Policy

A graduate employee who has violated any of the aforementioned assistantship policies or have received unsatisfactory performance evaluations may be subject to disciplinary action. The Department of Statistics will operate on a three-strike policy (three (3) violations), unless the actions are beyond correction or violate any University polices that may warrant full dismissal. The three-strike policy may take into consideration any and all performance evaluations that may be considered poor, engaging in unapproved time off that conflict with the obligation of the appointment offer, or other behavior that may be deemed unprofessional to that of the standing as a graduate employee.

When assistantship performance is unsatisfactory, the assistantship duties may be reduced and appointment fraction and pay may be reduced correspondingly, or the assistant may be dismissed. In cases where assistantship performance is unsatisfactory, the matter will first be discussed with the assistant prior to any action being taken. An assistant shall be given two (2) business days advance notice of such a discussion. An assistant shall be entitled to the presence of a Union Representative at such a discussion if the graduate employee has reasonable grounds to believe that the results of the discussion may be used to support disciplinary action against them and requests the Union representation.

Any graduate employee who receives three-strikes may be dismissed from their current assistantship appointments with the Department of Statistics, jeopardizing any future appointments within the department. A graduate employee will have the opportunity to appeal all grievances against them within a timely manner.

G.           Employment Dismissal

Dismissal is termination of an assistantship during a semester or other period of appointment. The parties recognize the authority of the University to dismiss or take other appropriate disciplinary action against an assistant for just cause, which shall include but not be limited to the following reasons: failing to attend mandatory orientation or other sessions; engaging in misconduct in the performance of University duties or academic activities; neglecting or refusing to perform assigned duties; demonstrating unsatisfactory performance; violating University regulations or policies; violating University regulations or policies related to discrimination and harassment; acting outside the appropriate exercise of University responsibilities so as willfully to physically harm, threaten physical harm to, harass or intimidate a visitor or a member of the University community with the effect of interfering with that person’s performance of University duties or academic activities; or damaging, destroying or misappropriating property owned by the University or any property used in connection with a University function or approved activity. Dismissal may result from an accumulation of minor infractions as well as for a single serious infraction. The assistant will be provided with written notice and an opportunity to respond to the Unit Executive Officer prior to dismissal. A supervisor alerted to the possibility of misconduct by an assistant shall attempt to resolve the issue and clarify the facts directly with the assistant. Discipline shall be issued in a private manner so as not to cause embarrassment to the assistant. Discipline short of dismissal may be taken which may include a Written Reprimand. A Written Reprimand shall state the facts supporting the discipline and be in the form of an official, signed letter. The assistant will be provided with an opportunity to respond to the supervisor and, if desired, to the Unit Executive Officer. Discipline in the form of a Written Reprimand is not required prior to seeking to dismiss an assistant. If any discipline is taken against an assistant, the assistant will receive a copy of the disciplinary action.

DFR: Deferred grades are issued at the end of the term only for STAT 599. DFR grades will only be changed to an “S” grade once the thesis has successfully be completed.  

I: Incomplete grades are issued at the end of the term when students have not completed the required work for the course. The time limit for students to complete the work is as follows:

• 5:00 PM of Reading Day of the next semester in which the student is registered, if next semester of registration is within a year
• if not registered in a graded course within a year, one year After the deadline, the Graduate College will automatically change an “I” grade to an “F by Rule”. This failing grade will be reflected in the student’s GPA until the instructor changes it. 

NR: Not reported. This temporary notation is automatically entered if an instructor does not report a grade by the deadline. A student will not be certified for a degree with an NR notation in the academic record.

S / U: Satisfactory / Unsatisfactory. A permanent notation used as a final grade only in courses (generally thesis research or seminar courses) approved for this grade mode.

W: Withdraw. A permanent notation signifying an approved withdraw without credit.

Department of Statistics

Statistics is a uniquely fascinating discipline, poised at the triple conjunction of mathematics, science, and philosophy.

As the first and most fully developed information science, it's grown steadily in influence for 100 years, combined now with 21st century computing technologies. What do statisticians do? Everything.

Ten Statistical Ideas That Changed the World

In this collection of videos, Trevor Hastie and Rob Tibshirani interview authors of seminal papers in the field of statistics. This project was part of Stanford's STATS 319 class held in Winter Quarter of 2024.

News & Announcements

• Department News

2024 Department Dissertation Awards

Project team receives first sds open source software prize, sourav chatterjee elected to aaas.

2024 Department Diploma Ceremony

Sunday, June 16th, 11:30am at Sequoia Hall Grove

Upcoming Seminars & Events

• Probability Seminar

The branching random walk subject to a hard-wall constraint

Industrial Affiliates

Our IA Program develops practical relationships between the department and the industrial community by creating opportunities for scientists, engineers, and developers from high-profile businesses to meet with our graduate students and share research topics in an informal setting. The annual conference for members, faculty, and final-year PhD candidates is a highlight event in our academic year.

Department Technical Reports

The entire collection of Tech Reports issued by the Statistics Department — since 1949 — is available in PDF format. Browse the Archive in date order or search by Author, Year, Series, or Title keyword: advance your research or just find something interesting every time!

To Improve Learning For Each Learner, Turn a Mirror on Your System

• Posted May 30, 2024
• By Lory Hough
• Career and Lifelong Learning
• K-12 System Leadership
• Organizational Change

When the Ed School’s Data Wise Project decided to publish a book nearly 20 years ago offering a step-by-step process for using data to improve teaching and learning in schools, their target audience was clear: educators in schools. The project had no intention of scaling the work beyond that group.

But eventually, something else became clear: While the Data Wise book and the initial data-related course they offered were huge hits, educators wanted — and needed — more guidance as they worked toward better serving students. Additional books followed, plus a group of professional learning offerings , ranging from a massive open online course (MOOC) to a coach certification program. 

“We put Data Wise out into the world and were very heartened by the reception of school-based people feeling like, oh, this is a model that can help me do my work better,” says Kathy Boudett , director of the Data Wise Project and a senior lecturer at the Ed School. “But pretty quickly, people at the system level who were supporting schools started asking, ‘What’s our role in modeling this work and supporting schools in doing it well?’”

To help answer these questions, the Data Wise Project staff decided it was time to capture what they’ve learned from working with systems, not just educators in schools, in a new book, out this month through Harvard Education Press called System Wise: Continuous Educational Improvement at Scale . Written by Adam Parrott-Sheffer, Ed.M.’09, Ed.L.D.’20; Carmen Williams, Ed.L.D.’22; David Rease, Jr., Ed.L.D.’14; and Boudett, System Wise extends the Data Wise process from individual classrooms and schools to broader educational contexts for educators at any level. Plans are also underway to launch the first System Wise Leadership Institute, which will take place in May 2025. 

One of the challenges that all system-level leaders face is how to think about scale. The Data Wise team was no different. When they attended the Scaling for Impact institute at the Ed School, “It was like someone turned on the lights,” they write in System Wise . “Until then, we had understood scaling to be about getting bigger, and we were hesitant to embrace growth for growth’s sake. Discovering that scaling could involve depth, sustainability, spread, shift, and evolution helped us to see that scaling didn’t mean we needed to water down our model in an effort to serve more people. In System Wise , we share this learning.”

That original model includes allowing educators to build the skills necessary for looking at data, identifying a problem, coming up with an action plan, and then assessing how well the plan is working to improve student learning. It lets educators dig deep and look not just at numbers, but also teaching practices. Team leaders, principals, and district administrators become “system wise” when, as the book points out, they cultivate the “ACE habits of mind” around action, collaboration, and evidence.

Williams, a school assistant superintendent of instruction and innovation and co-chair of the Data Wise in Action Program , says the ACE habits come from the Data Wise book, but they have evolved.

"What we’ve been able to do is talk about how critical practicing those [habits] are to building a culture around data,” she said in an interview with Harvard Education Press, the publisher of Data Wise and System Wise . “It’s not just doing Data Wise, it's being Data Wise. The Ace Habits of Mind help us to shift our mindsets, but also our orientation to the work of improvement cycles. I think that’s a game changer when you're at the system level because, typically, a system leader gives a directive and someone else follows it. If there's going to be a culture change, everyone is going to be rowing in the same direction. By committing to the Ace Habits of Mind, that's kind of the anchor for how we can all move together and have a rhythm. If we’re speaking the same language and we have the same mindsets, then at every level of the organization we’re deepening our practice around data.”

Each chapter of System Wise starts out with a question, such as, “What counts as data?” and “Do we see each learner first through their strengths?” which are designed to support taking an equity lens. Chapters also include case studies, planning checklists, implementation templates, and a discussion of what the approach looks like at each step. Parrott-Sheffer says the book allows readers to jump in at any point.

“We really think as you read System Wise, you’ll be like, ‘Hey, I'm at a stage where I'm trying to figure out what to focus on, so I might start at the beginning.’ You might already have a strategic plan you’ve built and you’re going to start with step six and seven, more towards the middle of the book, because that’s going to be most applicable. The nice thing about continuous improvement is you can join the carousel anywhere and it’s going to get you into the feedback loop.”

The work is also very student centered. Rease, director of equity, diversity, and belonging in Prince George’s County Public Schools in Maryland, points to chapter two of the book, where Jorge, an educator in Illinois, talks about how they were not setting high expectations for immigrant students in their district. As his system engaged in the improvement process, they realized they had “been doing school in the same way” and, with this new group of students, what they were doing might be harmful. “The System Wise approach created an opportunity for that reflection to happen,” Rease says, “so that people could start behaving differently and really assess their values.”

Another key aspect of the System Wise book, Williams says, is its focus on community.

“There are going to be people who pick this book up and feel affirmed because they’re already doing some of the practices,” she says. “The missing piece, though, might be how do you know to what level? To what end are you producing what you really want to produce? That’s where the value of reading this book and doing this book in community comes in. It’s just like a workout with a trainer. You can walk on the treadmill at a pace, but you might need someone else to say, ‘I bet you can go faster. I bet we can go longer.’ Reading this book and living this book in community is where you’re going to get the best results.”

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Josh Gibson becomes MLB career and season batting leader as Negro Leagues statistics incorporated

FILE - Baseball catcher Josh Gibson in an undated photo. Josh Gibson became Major League Baseball’s career leader with a .372 batting average, surpassing Ty Cobb’s .367, when records of the Negro Leagues for more than 2,300 players were incorporated after a three-year research project. (AP Photo/File)

The grave stone for baseball player Josh Gibson is shown at Allegheny Cemetery in Pittsburgh on March 17, 2017. Gibson became Major League Baseball’s career batting leader with a .372 average, surpassing Ty Cobb’s .367 when records of the Negro Leagues for more than 2,300 players were incorporated Tuesday, May 28, 2024, after a three-year research project. (AP Photo/Keith Srakocic, File)

FILE - Sean Gibson, the executive director of the Josh Gibson Foundation, poses next to a poster at the Pittsburgh Opera House in Pittsburgh for the upcoming opera about his great-grandfather, baseball player Josh Gibson, on March 17, 2017. Josh Gibson became Major League Baseball’s career batting leader with a .372 average, surpassing Ty Cobb’s .367 when records of the Negro Leagues for more than 2,300 players were incorporated Tuesday, May 28, 2024, after a three-year research project. (AP Photo/Keith Srakocic, File)

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NEW YORK (AP) — Josh Gibson became Major League Baseball’s career leader with a .372 batting average, surpassing Ty Cobb’s .367, when Negro Leagues records for more than 2,300 players were incorporated Tuesday after a three-year research project.

Gibson’s .466 average for the 1943 Homestead Grays became the season standard, followed by Charlie “Chino” Smith’s .451 for the 1929 New York Lincoln Giants. They overtook the .440 by Hugh Duffy for the National League’s Boston team in 1894.

Gibson also became the career leader in slugging percentage (.718) and OPS (1.177), moving ahead of Babe Ruth (.690 and 1.164).

“It’s a show of respect for great players who performed in the Negro Leagues due to circumstances beyond their control and once those circumstances changed demonstrated that they were truly major leaguers,” baseball Commissioner Rob Manfred said Wednesday in an interview with The Associated Press. “Maybe the single biggest factor was the success of players who played in the Negro Leagues and then came to the big leagues.”

AP AUDIO: Josh Gibson becomes MLB career and season batting leader as Negro Leagues statistics incorporated

AP Washington correspondent Sagar Meghani reports Major League Baseball’s record book looks a lot different, with Negro League records now incorporated.

A special committee on baseball records decided in 1969 to recognize six major leagues dating to 1876: the National (which launched in 1876), the American (1901), the American Association (1882-1891), Union Association (1884), Players’ League (1890) and Federal League (1914-1915). It excluded the National Association (1871-75), citing an “erratic schedule and procedures.”

MLB announced in December 2020 that it would be “correcting a longtime oversight” and would add the Negro Leagues . John Thorn, MLB’s official historian, chaired a 17-person committee that included Negro Leagues experts and statisticians.

“The condensed 60-game season for the 2020 calendar year for the National League and American League prompted us to think that maybe the shortened Negro League seasons could come under the MLB umbrella, after all,” Thorn said.

An updated version of MLB’s database will become public before the St. Louis Cardinals and San Francisco Giants play a tribute game to the Negro Leagues on June 20 at Rickwood Field in Birmingham, Alabama.

Baseball Hall of Fame President Josh Rawitch said statistics on Cooperstown plaques will remain the same because they reflect the information available at the time of a player’s induction.

Standards for season leaders is the same for Negro Leagues as the other leagues: 3.1 plate appearances or one inning for each game played by a player’s team.

Gibson’s .974 slugging percentage in 1937 becomes the season record, and Barry Bonds’ .863 in 2001 dropped to fifth, also trailing Mules Suttles’ .877 in 1926, Gibson’s .871 in 1943 and Smith’s .870 in 1929.

Bond’s prior OPS record of 1.421 in 2004 dropped to third behind Gibson’s 1.474 in 1937 and 1.435 in 1943.

Willie Mays gained 10 hits from the 1948 Birmingham Black Barons, increasing his total to 3,293. Minnie Minoso surpassed 2,000 hits, credited with 150 for the New York Cubans from 1946-1948 that boosted his total to 2,113.

Jackie Robinson, who broke MLB’s color barrier with the 1947 Dodgers, was credited with 49 hits with the 1945 Kansas City Monarchs that increased his total to 1,567.

Among pitchers, Satchel Paige gained 28 wins that raised his total to 125.

The committee met six times and dealt with issues such as when compiled league statistics didn’t make sense, such as a league having more wins than losses and walks that were missing. Researchers had to identify whether players with the same name were one person or separate, tracking dates of birth, and identify people listed by nicknames. Documenting transactions and identifying ballparks in a time when neutral sites often were used is ongoing, along with uncovering statistics for independent teams.

“We made the decision at a point in time that we became convinced that it was possible to get accurate statistics that could be appropriately integrated into our record books,” Manfred said.

Kevin Johnson and Gary Ashwill, researchers who had spent nearly two decades helping assemble the Seamheads Negro Leagues Database, were included in the project.

Thorn estimated 72% of Negro Leagues records from 1920-1948 are included and additional research might lead to future modifications. Thorn said a four-homer game by Gibson in 1938 and a home run by Mays in August 1948 could not be included because complete game accounts have not been found.

“Without a box score, we can’t really balance the statistics,” Johnson said. “Those games are kind of in limbo at the moment.”

Records include the first Negro National League (1920-31), Eastern Colored League (1923-28), American Negro League (1929), East-West League (1932), Negro Southern League (1932), second Negro National League (1933-48) and Negro American League (1937-48). Barnstorming exhibition games are not included.

Some game details were obtained from newspapers that covered the Black communities. Johnson said while complete accounts were found for about 95% of games in the 1920s, coverage dropped off during the Great Depression in the 1930s and never fully recovered.

AP MLB: https://apnews.com/hub/MLB

Inclusion of Negro Leagues statistics in MLB records only enhances baseball’s history

To anyone questioning the legitimacy of making Negro Leagues statistics part of Major League Baseball ’s official record, I pose this question:

How legitimate were MLB’s statistics prior to 1947, when the league was essentially an all-white men’s club?

If you want to argue Josh Gibson didn’t face the best competition, well, neither did Babe Ruth. And if you want to argue Gibson’s newly anointed record-setting 1943 season is less meaningful because he appeared in only 69 games, well, people who follow the sport are forever engaging in such context-driven debates.

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The question of whether Hank Aaron or Barry Bonds should be considered the all-time home-run leader is not exactly settled in the minds of many fans, is it?

I understand why some found it jarring to learn Wednesday that Gibson was the new all-time leader in batting average, slugging percentage and OPS. But I found it more jarring that MLB , before declaring the Negro Leagues a major league in 2020, did not fully acknowledge a generation of elite Black professional players.

That’s what this is all about, really – acknowledging that Gibson and Oscar Charleston and Turkey Stearnes deserve the same recognition as Ruth, Ty Cobb, Honus Wagner and other pre-1947 greats.

Yes, Gibson, Charleston and Stearnes are among the Negro Leagues players in the Hall of Fame. The difference now is their statistics will be a formal part of the baseball narrative, increasing awareness, sparking curiosity. As Reds pitcher Hunter Greene put it, “I’m going to have to do a little bit more research and understand some of the history to kind of rewire my brain on some of the best players.”

Several Major League records are now held by Josh Gibson as he and other Negro Leagues legends officially join the all-time leaderboards. The statistics of more than 2,300 Negro Leagues players launch today in a newly integrated https://t.co/Z3s2EpgF39 database that presents… pic.twitter.com/UyvCu0pSzi — MLB (@MLB) May 29, 2024

“People will be, I don’t know if upset is the right word, but they may be uncomfortable with some Negro League stars now on the leaderboards for career and seasons,” Larry Lester, an author and longtime Negro Leagues researcher, told The Athletic’s Tyler Kepner . “Diehards may not accept the stats, but that’s OK. I welcome the conversations at the bar or the barbershop at the pool hall. That’s why we do what we do.”

Lester was part of a 17-person committee, comprised of historians, writers and statisticians, as well as a former player and GM, that determined which Negro Leagues games counted toward the official record. The sole goal of the committee members was to achieve historical accuracy. Some worked tirelessly to document Negro League records even before MLB became interested. And the committee will continue trying to assemble the most complete account of Negro Leagues games possible, adjusting as more information becomes available.

Blasphemy, you say? Numbers are immutable?

As The Athletic’s Marc Carig wrote in 2021 , “No official records of the American League exist before 1905. For a period in the 1910s, the National League recorded win-loss records for pitchers. But the American League did not, because league president Ban Johnson believed them to be a poor judge of a pitcher’s performance. When the RBI became an official statistic in 1920, some scorers did not understand the rule, leading to chaos in the records.”

Such gaps in information are nothing new. Ty Cobb’s career totals for runs, hits and batting average vary (though admittedly not by much), depending upon the source. The 60-game COVID season in 2020 disrupted the standard 162-game record-keeping. So did, ahem, the strike-shortened seasons in 1981, 1994 and ‘95.

The Negro Leagues presented a different challenge for those trying to set the record straight, not only in uncovering the right information, but also in determining which information to use. Yet take it from John Thorn, 77, who has been MLB’s official historian since 2011. None of this work would have been necessary if baseball had not been segregated in the first place.

“Shortened Negro League schedules, interspersed with revenue-raising exhibition games, were born of MLB’s exclusionary practices,” said Thorn, who headed the statistical review committee. “To deny the best Black players of the era their rightful place among all-time leaders would be a double penalty.”

But for more than half a century, that penalty was in effect.

When the Special Baseball Records Committee (SBRC) first assembled in 1968-69, the group never considered or discussed the Negro Leagues. It recognized not only the NL (1876 to the present), the AL (1901 to the present) but also four other leagues that existed between 1882 and 1915. Against that backdrop, excluding the Negro Leagues was even more illogical.

Why not acknowledge Negro Leagues statistics, but keep them separate from MLB’s? This strikes at a sensitive issue. Any celebration of MLB’s embrace of the Negro Leagues should be muted, considering how long the league kept out Black players. The merging of stats risks glossing over that point. It’s a complex question without an easy answer. Still, the idea is to end separation, not perpetuate it.

Why not make stats from the Japanese, Korean and other foreign leagues official as well? When I asked Thorn about that, he said he anticipated such “conceptual drift.” The difference, he added, is that none of those leagues offers the evidence of major-league caliber play required by MLB – though Japan’s Nippon Professional Baseball (NPB), in his estimation, is inching closer. The current version of NPB also did not take shape until 1950, after MLB’s color line was broken.

Baseball’s history is what separates it from other sports. Fans compare players from different eras, trying to figure out who was best. These comparisons are almost always imperfect, apples to oranges. And so it will be with Negro Leagues players. I can’t say if Josh Gibson was better than Babe Ruth. But I’m sure eager to advance the discussion.

(Top photo of Josh Gibson sliding into home at East-West All-Star Game of the Negro Leagues in 1944 at Comiskey Park: Bettmann/Getty Images)

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Ken Rosenthal is the senior baseball writer for The Athletic who has spent nearly 35 years covering the major leagues. In addition, Ken is a broadcaster and regular contributor to Fox Sports' MLB telecasts. He's also won Emmy Awards in 2015 and 2016 for his TV reporting. Follow Ken on Twitter @ Ken_Rosenthal

Watch CBS News

Statistics from Negro Leagues officially integrated into MLB record books

By Faris Tanyos

Updated on: May 29, 2024 / 8:57 PM EDT / CBS News

In a milestone decision decades in the making, Major League Baseball announced Tuesday that it is now incorporating statistics of Negro Leagues that operated in the 1920s, 1930s and 1940s into its record books.  

"This initiative is focused on ensuring that future generations of fans have access to the statistics and milestones of all those who made the Negro Leagues possible," MLB Commissioner Rob Manfred said in a statement provided to The Associated Press. 

Black players were barred from MLB until Jackie Robinson broke the league's color barrier in 1947 when he joined the Brooklyn Dodgers. That breakthrough ultimately led to the Negro Leagues ending play in 1960.

"Their accomplishments on the field will be a gateway to broader learning about this triumph in American history and the path that led to Jackie Robinson's 1947 Dodger debut," Manfred said in his statement.

In 2020, in the wake of America's reckoning with racial injustice following the murder of George Floyd, MLB announced that it was "elevating" seven Negro Leagues that operated from 1920 to 1948 to "major league" status, a move which, at the time, meant approximately 3,400 players in those Negro Leagues could be recognized by MLB for their on-field achievements. Wednesday's announcement, however, will take that a step further.

The immediate impact of the incorporation will see Josh Gibson, one of baseball's greatest players, take multiple records from the likes of Ty Cobb and Babe Ruth, per CBS Sports.

Gibson will become the all-time leader in career batting average at .372, passing Cobb's mark of .366, according to CBS Sports. His career .718 slugging percentage will also be the all-time high mark now, surpassing Ruth's previous record of .690, and he'll be the leader in career OPS (on-base plus slugging percentage) with 1.177, passing Ruth's mark of 1.164.

"When you hear Josh Gibson's name now, it's not just that he was the greatest player in the Negro Leagues, but one of the greatest of all time," Sean Gibson, Gibson's great-grandson, told USA Today in a statement Tuesday. "These aren't just Negro League stats. They're major-league baseball stats."

In 2020, MLB acknowledged that it was seeking to rectify a 1969 decision by the Special Committee on Baseball Records — a group that was formed to determine which leagues would be recognized as "major leagues." That 1969 committee recognized six such "major leagues" dating back to 1876, but omitted all Negro Leagues from consideration.

"It is MLB's view that the committee's 1969 omission of the Negro Leagues from consideration was clearly an error that demands today's designation," the league said in 2020.

The late Hank Aaron played in the Negro Leagues before entering MLB and eventually breaking Ruth's career home run record. In the 2023 documentary "The League," he described the challenges Negro League players faced.

"We got one dollar a day meal money, and we would buy one loaf of bread and we would buy a big jar of peanut butter," Aaron said. "That's what we lived off of for three or four days."

— Zoe Christen Jones and Jericka Duncan contributed to this report. 

• Major League Baseball
• Jackie Robinson

Faris Tanyos is a news editor for CBSNews.com, where he writes and edits stories and tracks breaking news. He previously worked as a digital news producer at several local news stations up and down the West Coast.

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