statistics phd textbooks

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!

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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.

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Mathematics: textbooks (math and statistics).

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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

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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

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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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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 during the spring semester of Year 2 or the fall semester 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.

Statistics for Research Students

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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.

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

• Submit ancillary resource

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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• © 2022

Statistics for Data Scientists

An Introduction to Probability, Statistics, and Data Analysis

• Maurits Kaptein 0 ,
• Edwin van den Heuvel 1

Tilburg University, Tilburg, The Netherlands

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Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

Provides an accessible introduction to applied statistics by combining hands-on exercises with mathematical theory

Introduces statistical inference in a natural way, using finite samples and real data

Contains modern statistical methods including Bayesian decision theory, equivalence testing and statistical modelling

Part of the book series: Undergraduate Topics in Computer Science (UTICS)

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Table of contents (9 chapters)

Front matter, a first look at data.

• Maurits Kaptein, Edwin van den Heuvel

Sampling Plans and Estimates

• Probability Theory

Random Variables and Distributions

Multiple random variables, making decisions in uncertainty, bayesian statistics, correction to: statistics for data scientists.

This book provides an undergraduate introduction to analysing data for data science, computer science, and quantitative social science students. It uniquely combines a hands-on approach to data analysis – supported by numerous real data examples and reusable [R] code – with a rigorous treatment of probability and statistical principles. 

• Data Science
• Random Variables
• Statistical Testing
• Statistical Methods
• Data Analysis

Maurits Kaptein

Edwin van den Heuvel

Book Title : Statistics for Data Scientists

Book Subtitle : An Introduction to Probability, Statistics, and Data Analysis

Authors : Maurits Kaptein, Edwin van den Heuvel

Series Title : Undergraduate Topics in Computer Science

DOI : https://doi.org/10.1007/978-3-030-10531-0

Publisher : Springer Cham

eBook Packages : Computer Science , Computer Science (R0)

Copyright Information : Springer Nature Switzerland AG 2022

Softcover ISBN : 978-3-030-10530-3 Published: 03 February 2022

eBook ISBN : 978-3-030-10531-0 Published: 02 February 2022

Series ISSN : 1863-7310

Series E-ISSN : 2197-1781

Edition Number : 1

Number of Pages : XXIV, 321

Number of Illustrations : 34 b/w illustrations, 19 illustrations in colour

Topics : Probability and Statistics in Computer Science , Statistical Theory and Methods , Probability Theory and Stochastic Processes

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Looking for a good and complete probability and statistics book

I never had the opportunity to visit a stats course from a math faculty. I am looking for a probability theory and statistics book that is complete and self-sufficient. By complete I mean that it contains all the proofs and not just states results. By self-sufficient I mean that I am not required to read another book to be able to understand the book. Of course it can require college level (math student) calculus and linear algebra.

I have looked at multiple books and I didn't like any of them.

DeGroot & Schervish (2011) Probability and Statistics (4th Edition) Pearson

This is not complete enough. It just states a lot of stuff without the derivation. Besides that I like it.

Wasserman (2004) All of Statistics: A Concise Course in Statistical Inference Springer.

Didn't like it at all. Almost no explanations.

"Weighing the Odds" from David Williams is more formal than DeGroot and seems to be complete and self-sufficient. However, I find the style strange. He also invents new terms that only he seems to use. All the stuff that is explained in DeGroot too is explained better there.

If you know a great book in German that's also fine as I am German.

• probability
• mathematical-statistics
• 4 $\begingroup$ What level of text are you looking for? I think that Degroot book is aimed more at undergraduate students. A good book for graduate level studies is Statistical Infernece by Casella and Berger. $\endgroup$ –  user25658 Sep 19, 2013 at 22:17
• 15 $\begingroup$ This definition of "self sufficient" is subjective, because your ability to "understand the book" depends on your background. $\endgroup$ –  whuber ♦ Sep 20, 2013 at 1:44
• 4 $\begingroup$ I'm guessing that there is no book that you will find completely satisfactory. $\endgroup$ –  mark999 Sep 20, 2013 at 9:18
• 2 $\begingroup$ Self sufficient given the knowledge that you have after obtaining a bachelor in mathematics. With regards to the topics Degroot is what I am looking for but I don't like books in which core results (e.g. chi square distribution of the test statistics given the null hypothesis is true for the likelihood ratio test) are not derived. I will have a look at Statistical Inference by Casella and Berger. $\endgroup$ –  Julian Karch Sep 20, 2013 at 11:25
• 7 $\begingroup$ How can a book on probability and statistics ever be complete ? Even huge multi-volume tomes (Kendall and Stuart's .. etc's Advanced theory of Statistics in its latest incarnations, for example, come to thousands of pages if I recall correctly) aren't remotely complete. $\endgroup$ –  Glen_b Sep 21, 2013 at 1:36

8 Answers 8

If you are searching for proofs, I have been working for some time on a free stats textbook that collects lots of proofs of elementary and less elementary facts that are difficult to find in probability and statistics books (because they are scattered here and there). You can have a look at it at http://www.statlect.com/

• $\begingroup$ Why are they scattered here and there? I thought teaching statistics is supposed to be systematic. $\endgroup$ –  Cheng Apr 27 at 0:17
• $\begingroup$ @Cheng. It probably is, statistically speaking. $\endgroup$ –  Mad Physicist Jun 12 at 2:12

If you want to read probability as a story, read the best book ever by Feller . I am also guessing that you do not want to go to the level of measure theoretic definition of probabilities which has specialized books. another beginner level book is from Ross . Other specialized applications have specialized books. so more information will gather better suggestions.

I would recommend two books not mentioned, as well as several already mentioned.

The first is E.T. Jaynes "Probability: The Language of Science." It is polemic and he is a very partisan author, but it is very good.

The second is Leonard Jimmie Savage's "The Foundations of Statistics." You will probably be very surprised when you first start reading it as you will not expect it to go the route it goes.

Both are writing foundational work in Bayesian probability and Bayesian statistics. The above works are non-Bayesian.

Both books are completely contained and self-sufficient. Indeed, they build from the foundation upward. Both approach it axiomatically.

• 2 $\begingroup$ Well don't leave us in suspense, what is the unexpected route that Savage's book follows? $\endgroup$ –  Praxeolitic Oct 26, 2017 at 1:40
• 2 $\begingroup$ @Praxeolitic Savage grounds his book in preference theory. You construct a strictly "personalistic" basis for probability and statistics. What is as interesting is that these measures are intrinsically admissible statistics, whereas that is not automatically true for non-Bayesian methods. $\endgroup$ –  Dave Harris Nov 8, 2017 at 0:04

Finding a single, comprehensive book will be very difficult. If you're asking because you want to do some self-study, get a couple of used texts instead of a single new one. You can get classics for $3-10 dollars if you look around online.

Feller's "Introduction to Probability" is great for its completeness and expository style, but I don't like the exercises much. And the exposition would not make it so good for a reference. He tends to have a lot of long examples, which is great for fostering understanding, and not so great for looking things up.

I enjoyed Allan Gut's "An Intermediate Course in Probability". There is some overlap with Feller, but it goes into greater depth on those topics. He covers the various transformations, order statistics (which, if I recall, Feller only does by example).

Ross' Introduction to Probability Models is pretty comprehensive, but it is very example oriented. Again, that is not my favorite style (I'd rather they saved those examples for exercises with hints, and kept them out of the main flow), but if it works for you, I can recommend it.

You might as well consider Cacoullos' "Exercises in Probability" and Mosteller's "50 Challenging Exercises in Probability".

For the probability side I like Probability and Random Processes by Grimmett & Stirzaker. It has a nice way of giving intuitive explanations whilst still being fairly rigorous and providing some proofs at least.

For the Statistics side I've had Theory of Statistics by Schervish on my wish list for a while now but not got around to buying it, so I can only say I've heard good things about it...it's supposed to be a graduate level introduction so possibly more rigorous than the other Schervish book you mention.

• $\begingroup$ +1 for Theory of Statistics by Schervish. It is an excellent book for anyone who is well versed with measure-theoretic probability and wants an almost complete statistics book. $\endgroup$ –  Aditya Sep 24, 2020 at 3:09

I recommend Probability Theory and Mathematical Statistics by Marek Fisz, because:

• It contains most of the common proof, but without making the book too difficult as an introduction book
• It is quite theoretical, but still contain enough well-designed examples to illustrate points
• Exercises are meaningful. Some of them are more advanced famous results

As noted by many others, there is no single good text for any scientific subject simply because any given authors or group of authors use a set of assumptions regarding the readers' level of understanding and diversity of knowns and unknowns in the user's brain. Said this, my suggestion for someone knows basics in calculus and linear algebra is to begin with the "modern mathematical statistics with applications" by Devore and Berk .

• $\begingroup$ Since you mentioned Devore, I want to know your opinion of his other well-known book : Probability and Statistics for Engineering and the Sciences by Jay L. Devore. Among other similar books, I think I will use it as the main textbook. Others such as by Sheldon Ross's book, Morris DeGroot's book, Miller and Freunds's book are really interesting, though, but I will go to the former first. I had learnt this subject about 33 years ago, but mostly for passing the exam. So I need to relearn it in the correct manner. $\endgroup$ –  Lex Soft Jul 6, 2022 at 2:56

You can read Student's Solutions Guide for Introduction to Probability, Statistics, and Random Processes book. It provides clear examples and exercises with "additional questions" at the end of each chapter which really help improve learning and there is a logical progression from one idea to another.

Not the answer you're looking for? Browse other questions tagged probability self-study mathematical-statistics references or ask your own question .

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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

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Statistics, 4th Edition 4th Edition

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Renowned for its clear prose and no-nonsense emphasis on core concepts, Statistics covers fundamentals using real examples to illustrate the techniques.

• ISBN-10 0393929728
• ISBN-13 978-0393929720
• Edition 4th
• Publisher W. W. Norton & Company
• Publication date February 13, 2007
• Language English
• Dimensions 7.4 x 1.4 x 10.4 inches
• Print length 720 pages
• See all details

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• Publisher ‏ : ‎ W. W. Norton & Company; 4th edition (February 13, 2007)
• Language ‏ : ‎ English
• Hardcover ‏ : ‎ 720 pages
• ISBN-10 ‏ : ‎ 0393929728
• ISBN-13 ‏ : ‎ 978-0393929720
• Item Weight ‏ : ‎ 2.77 pounds
• Dimensions ‏ : ‎ 7.4 x 1.4 x 10.4 inches
• #94 in Dermatology (Books)
• #168 in Statistics (Books)
• #506 in Probability & Statistics (Books)

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About the author

David freedman.

David A. Freedman (1938-2008) was a Professor of Statistics at the University of California, Berkeley. A distinguished mathematical statistician, he revolutionized the teaching of statistics with his undergraduate (new edition, 2007) and graduate (new edition, 2009) textbooks that emphasize clear reasoning over mere technique and that use numerous illustrations and empirical examples that are vivid, real, and up-to-date. Freedman also published widely on the application--and misapplication--of statistics in the social sciences. This major aspect of his work is synthesized in his book "Statistical Models and Causal Inference" (2009). Freedman was a member of the American Academy of Arts and Sciences and in 2003 received the National Academy of Science's John J. Carty Award for his "profound contributions to the theory and practice of statistics."

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Textbook assignments for spring 2023, summer 2023, and fall 2023 are listed below. Thanks to the  Cornell Mathematics Library , free e-versions of textbooks are available (and linked below) for many upper-level and graduate courses in mathematics.

Launching with the Fall 2022 semester, the Cornell Academic Materials Program is a university-wide program that provides undergraduate students taking undergraduate courses at Cornell with access to their required textbooks and coursepacks  for a single flat-rate cost, $225 per semester. All materials in this program are provided in a digital format within Canvas and become available for students to access no later than the first day of classes. Optional, out-of-print, and hard-to-find titles are not included in the program and will not be stocked at The Cornell Store.

MATH 1002 - PSSP Calculus Preparation and Quantitative Methods  // summer 2023

Lial, Greenwell, and Ritchey, Calculus with Applications, 11th edition, Pearson Education, 2016 (ISBN: 978-0-321-97942-1).

MATH 1003 - PSSP Statistics Preparation and Quantitative Methods  // summer 2023

Lial, Greenwell, and Ritchey, Finite Mathematics, 11th edition, Pearson Education, 2016 (ISBN: 978-0-321-97943-8).

MATH 1101 - Calculus Preparation  // fall 2023

No required textbook. The instructor may provide notes, references, or links to on-line resources.

MATH 1105 - Finite Mathematics for the Life and Social Sciences  // fall 2023

Lial, Greenwell, and Ritchey, Finite Mathematics, 12th edition, Pearson Education, 2022 (ISBN: 978-0-13-588262-7)

MATH 1106 - Modeling with Calculus for the Life Sciences  // spring 2023

Garfinkel, Shevtsov, and Guo, Modeling Life: The Mathematics of Biological Systems , Springer, 2017 (ISBN: 978-3-319-59730-0) — free e-book through the Cornell Math Library

MATH 1110 - Calculus I  // fall 2023, spring 2023

Boelkins, Matthew, Active Calculus 2018 , CreateSpace Independent Publishing, 2018 (ISBN: 978-1724458322).

MATH 1110 - Calculus I  //summer 2023

Hass, Heil, and Weir, Thomas’ Calculus: Early Transcendentals, Single Variable, 14th edition, Pearson Education, 2018 (ISBN: 978-0-13-443941-9) —  Instant Access  through  Canvas

MATH 1120 - Calculus II  // fall 2023, spring 2023

Math 1300 - mathematical explorations  // fall 2023.

Kalman, Forgoston, and Goetz, Elementary Mathematical Models: An Accessible Development without Calculus, 2nd edition, American Mathematical Society, 2019 (ISBN: 978-1-4704-5001-4).

MATH 1340 - Strategy, Cooperation, and Conflict  // spring 2023

Dixit, Skeath, and Reiley, Games of Strategy, 5th edition, W. W. Norton and Company, 2020 (ISBN: 978-0-393-42219-1).

MATH 1710 - Statistical Theory and Application in the Real World  // fall 2023, spring 2023

Diez, Barr, and Çetinkaya-Rundel, OpenIntro Statistics, 3rd edition, OpenIntro, Inc., 2015 (Edition: 3; ISBN: 978-1-943450-03-9) — available through  Canvas

MATH 1910 - Calculus For Engineers  // fall 2023, spring 2023, summer 2023

Rogawski, Adams, and Franzosa, Calculus, 4th edition, W. H. Freeman, 2019 (ISBN: 978-1-319-05073-3) —  Instant Access  through  Canvas

MATH 1920 - Multivariable Calculus For Engineers  // fall 2023, spring 2023, summer 2023

ALTERNATIVE for students who do not need access to material covered in MATH 1910: Rogawski, Adams, and Franzosa, Calculus: Late Transcendentals Multivariable, W. H. Freeman, 2019 (ISBN: 978-1-319-05578-3).

MATH 2130 - Calculus III  // spring 2023

Hughes-Hallett, et al, Calculus: Single and Multivariable, 7th edition, John Wiley & Sons, 2017 (ISBN: 978-1-119-32049-4).

MATH 2210 - Linear Algebra  // fall 2023, spring 2023

W. Keith Nicholson, Linear Algebra with Applications , Version 2021 Revision A (Open Edition)

MATH 2220 - Multivariable Calculus  // fall 2023, spring 2023

Shimamoto, Don, Multivariable Calculus , 2019 (ISBN: 978-1-7082-4699-0).

MATH 2230 - Theoretical Linear Algebra and Calculus  // fall 2023

Hubbard and Hubbard, Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach, 5th edition, Matrix Editions, 2015 (ISBN: 978-0-9715766-8-1).

(optional) Hubbard and Hubbard, Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach, 5th edition, Student Solutions Manual, Matrix Editions, 2015 (ISBN: 978-0-9715766-9-8).

MATH 2240 - Theoretical Linear Algebra and Calculus  // spring 2023

Math 2930 - differential equations for engineers  // fall 2023, spring 2023, summer 2023.

Boyce, DiPrima, and Meade, Elementary Differential Equations and Boundary Value Problems, 12th edition, John Wiley & Sons, 2021 (ISBN: 978-1-119-77769-4).

MATH 2940 - Linear Algebra for Engineers  // fall 2023, spring 2023, summer 2023

Lay, Lay, and McDonald, Linear Algebra and its Applications, 6th edition, Pearson Education, 2020 (ISBN: 978-0-13-684748-9).

MATH 3040 - Prove It!  // fall 2023

Velleman, Daniel J., How to Prove It: A Structured Approach, 3rd edition, Cambridge University Press, 2019 (ISBN: 978-1-108-43953-4).

MATH 3040 - Prove It!  // spring 2023

Beck and Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics , Springer (ISBN: 978-1-4419-7022-0) — free e-book through the Cornell Math Library

MATH 3110 - Introduction to Analysis  // fall 2023, spring 2023

Abbott, Stephen, Understanding Analysis, 2nd edition , Springer-Verlag, 2002 (ISBN: 978-1-4939-2711-1) — free e-book through the Cornell Math Library

MATH 3210 - Manifolds and Differential Forms  // fall 2023

Reyer Sjamaar, Manifolds and Differential Forms

MATH 3270 - Introduction to Ordinary Differential Equations  // fall 2023

Ahmad and Ambrosetti, A Textbook on Ordinary Differential Equations, 2nd edition , Springer, 2015 (ISBN: 978-3-319-16407-6) — free e-book through the Cornell Math Library

MATH 3320 - Introduction to Number Theory  // fall 2023, spring 2023

Jones and Jones, Elementary Number Theory , Springer, 1998 (ISBN: 978-3-540-76197-6) — free e-book through the Cornell Math Library

MATH 3340 - Abstract Algebra  // fall 2023, spring 2023

Beachy and Blair, Abstract Algebra, 4th edition, Waveland Press, Inc., 2019 (ISBN: 978-1-4786-3869-8)

MATH 3360 - Applicable Algebra  // spring 2023

Math 3610 - mathematical modeling  // fall 2023, math 4130 - honors introduction to analysis i  // fall 2023, math 4130 - honors introduction to analysis i  // spring 2023.

Lang, Serge, Undergraduate Analysis, 2nd edition , Springer, 1997 (ISBN: 978-0-387-94841-6) — free e-book through the Cornell Math Library

MATH 4140 - Honors Introduction to Analysis II  // spring 2023

Strichartz, Robert, The Way of Analysis (revised edition), Jones & Bartlett Publishers, 2000 (ISBN: 0-7637-1497-6).

MATH 4180 – Complex Analysis  // spring 2023

Silverman, Richard A., Complex Analysis with Applications, Dover Publications, 2010 (ISBN: 978-0-486-64762-3).

MATH 4200 - Differential Equations and Dynamical Systems  // fall 2023

Hubbard & West, Differential Equations:  A Dynamical Systems Approach; Vol I:  Ordinary Differential Equations , Springer-Verlag, 1995 (ISBN: 0-387-97286-2) — free e-book through the Cornell Math Library

Hubbard & West, Differential Equations: A Dynamical Systems Approach; Vol II: Higher-Dimensional Systems , Springer-Verlag, 1995 (ISBN: 0-387-94377-3) — free e-book through the Cornell Math Library

MATH 4210 - Nonlinear Dynamics and Chaos  // spring 2023

Strogatz, Steven H., Nonlinear Dynamics and Chaos with applications to Physics, Biology, Chemistry, and Engineering, 2nd edition, Westview Press, 2014 (ISBN: 978-0-8133-4910-7)

MATH 4220 - Applied Complex Analysis  // fall 2023

Asmar and Grafakos, Complex Analysis with Applications , Springer, 2018 (ISBN: 978-3-030-06788-5) — free e-book through the Cornell Math Library

Gamelin, Theodore W., Complex Analysis , Springer-Verlag, 2000 (ISBN: 0-387-95069-9) — free e-book through the Cornell Math Library

MATH 4250 - Numerical Analysis and Differential Equations  // fall 2023

Süli and Mayers, An Introduction to Numerical Analysis , Cambridge University Press, 2003 (ISBN: 978-0-521-81026-5) — free e-book through the Cornell Math Library

MATH 4280 - Introduction to Partial Differential Equations  // spring 2023

Salsa, Sandro, Partial Differential Equations in Action: From Modelling to Theory, 3rd edition , Springer, 2016 (ISBN: 978-3-319-31237-8) — free e-book through Cornell Math Library

MATH 4310 - Linear Algebra  // fall 2023

Axler, Sheldon, Linear Algebra Done Right, 3rd edition , Springer, 2015 (ISBN: 978-3-319-11079-0) — free e-book through the Cornell Math Library

MATH 4310 - Linear Algebra  // spring 2023

Friedberg, Insel, and Spence, Linear Algebra, 5th edition, Prentice Hall PTR, 2018 (ISBN: 978-0-13-486024-4).

MATH 4330 - Honors Linear Algebra  // fall 2023

Roman, Steven, Advanced Linear Algebra, 3rd edition , Springer, 2007 (ISBN: 978-0-387-72828-5) — free e-book through the Cornell Math Library

MATH 4340 - Honors Introduction to Algebra  // spring 2023

Dummit and Foote, Abstract Algebra, 3rd edition, John Wiley & Sons, 2004 (ISBN: 0-471-43334-9).

Silverman, Joseph H., Abstract Algebra: An Integrated Approach, American Mathematical Society, 2022 (ISBN: 978-1-4704-6860-6).

MATH 4370 - Computational Algebra // fall 2023

Cox, Little, and O'Shea, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 4th edition , Springer-Verlag, 2015 (ISBN: 978-3-319-16720-6) — free e-book through the Cornell Math Library

MATH 4410 - Introduction to Combinatorics I  // fall 2023

Bona, Miklos, A Walk Through Combinatorics: an introduction to enumeration and graph theory, 4th edition, World Scientific, 2017 (ISBN: 978-981-3148-84-0).

MATH 4500 - Matrix Groups  // spring 2023

Tapp, Kristopher, Matrix Groups for Undergraduates, 2nd edition , American Mathematical Society, 2016 (ISBN: 978-1-470-42722-1).

MATH 4520 - Classical Geometries // fall 2023

Math 4530 - introduction to topology  // fall 2023.

Munkres, James, Topology, 2nd edition, Prentice Hall PTR, 2000 (ISBN: 0-13-181629-2).

MATH 4540 - Introduction to Differential Geometry  // spring 2023

Pressley, Andrew, Elementary Differential Geometry, 2nd edition , Springer-Verlag, 2010 (ISBN: 978-1-84882-890-2) — free e-book through the Cornell Math Library

MATH 4550 - Applicable Geometry  // spring 2023

Connelly and Guest, Frameworks, Tensegrities, and Symmetry , Cambridge University Press, 2022 (ISBN: 978-0-521-87910-1) — free e-book through the Cornell Math Library

(optional) Ziegler, Gunter, Lectures on Polytopes , Springer-Verlag, 1994 (ISBN: 0-387-94365-X) — free e-book through the Cornell Math Library

MATH 4710 - Basic Probability  // fall 2023, spring 2023

Anderson, Seppalainen, and Valko, Introduction to Probability, Cambridge University Press, 2017 (ISBN: 978-1-108-41585-9)

MATH 4720 - Statistics  // spring 2023

Rice, John A., Mathematical Statistics and Data Analysis, 3rd edition, Brooks/Cole, 2007 (ISBN: 0-534-39942-8)

MATH 4740 - Stochastic Processes  // spring 2023

Durrett, Richard, Essentials of Stochastic Processes, 3rd edition , Springer, 2016 (ISBN: 978-3-3194-5613-3) — free e-book through the Cornell Math Library

MATH 4860 - Applied Logic  // fall 2023

Nerode and Shore, Logic for Applications, 2nd edition , Springer, 1997 (0-387-94893-7) — free e-book through the Cornell Math Library

MATH 5200 - Differential Equations and Dynamical Systems  // fall 2023

Math 5220 - applied complex analysis  // fall 2023, math 5250 - numerical analysis and differential equations  // fall 2023, math 5410 - introduction to combinatorics i  // fall 2023, math 6110 - real analysis  // fall 2023.

Stein and Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Princeton University Press, 2005 (ISBN: 0-691-11386-6).

MATH 6120 - Complex Analysis  // spring 2023

Stein and Shakarchi, Complex Analysis, Princeton University Press, 2003 (ISBN: 0-691-11385-8).

MATH 6150 - Partial Differential Equations  // fall 2023

Evans, Lawrence, Partial Differential Equations, 2nd edition, American Mathematical Society, 2010 (ISBN: 978-0-8218-4974-3).

MATH 6210 - Measure Theory and Lebesgue Integration  // fall 2023

Bartle, Robert, The Elements of Integration and Lebesgue Measure , John Wiley & Sons, 1966 (ISBN: 0-471-04222-6) — free e-book through the Cornell Math Library

MATH 6230 - Differential Games and Optimal Control  // spring 2023

Math 6270 - applied dynamical systems  // spring 2023.

Guckenheimer and Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields , Springer-Verlag, 1983 (ISBN: 0-387-90819-6) — free e-book through the Cornell Math Library

MATH 6310 - Algebra  // fall 2023

Isaacs, I. Martin, Algebra: a graduate course , American Mathematical Society, 2009 (ISBN: 978-0-8218-4799-2) — free e-book through the Cornell Math Library

MATH 6320 - Algebra  // spring 2023

Math 6370 - algebraic number theory  // spring 2023, math 6390 - lie groups and lie algebras  // fall 2023.

Hilgert and Neeb, Structure and Geometry of Lie Groups , Springer, 2012 (ISBN: 978-1-4899-9006-8) — free e-book through the Cornell Math Library

MATH 6410 - Enumerative Combinatorics // fall 2023

(optional) Stanley, Richard, Enumerative Combinatorics, Vol. I, 2nd edition , Cambridge University Press, 2011 (1-107-60262-9) — free e-book through the Cornell Math Library

(optional) Stanley, Richard P., Enumerative Combinatorics, Vol. 2, Cambridge University Press, 1998 (0-521-56069-1)

(optional) Aigner, Martin, A Course in Enumeration , Springer, 2007 (978-3-540-39032-9) — free e-book through the Cornell Math Library

MATH 6510 - Algebraic Topology  // spring 2023

Hatcher, Allen, Algebraic Topology , Cambridge University Press, 2001 (0-521-79540-0).

MATH 6520 - Differentiable Manifolds  // fall 2023

Math 6620 - riemannian geometry  // spring 2023.

Lee, John M., Introduction to Riemannian Manifolds, 2nd edition , Springer, 2018 (ISBN: 978-3-030-80106-9) — free e-book through the Cornell Math Library

MATH 6640 - Hyperbolic Geometry // fall 2023

Thurston, William P., Three-Dimensional Geometry and Topology, vol. 1 , Princeton University, 1997 (ISBN: 0-691-08304-5) — free e-book through the Cornell Math Library

MATH 6670 - Algebraic Geometry  // spring 2023

Hartshorne, Robin, Algebraic Geometry , Springer, 1977 (ISBN: 0-387-90244-9) — free e-book through the Cornell Math Library

MATH 6710 - Probability Theory I  // fall 2023

Durrett, Rick, Probability: Theory and Examples, 5th edition , Cambridge University Press, 2019 (ISBN: 978-1-108-47368-2) — free e-book through the Cornell Math Library

MATH 6720 - Probability Theory II  // spring 2023

Durrett, Rick, Probability: Theory and Examples, 5th edition , Cambridge University Press, 2019 (ISBN: 978-1-108-47368-2) — free e-book through the Cornell Math Library

MATH 6740 - Mathematical Statistics II  // fall 2023

Korostelev and Korosteleva, Mathematical Statistics: Asymptotic Minimax Theory , American Mathematical Society, 2011 (ISBN: 978-0-8218-5283-5) — free e-book through the Cornell Math Library

MATH 6810 - Logic  // spring 2023

Math 6830 - model theory  // fall 2023.

Marker, David, Model Theory: An Introduction , Springer, 2002 (ISBN: 0-387-98760-6) — free e-book through the Cornell Math Library

MATH 7110 - Topics in Analysis: Geometric Analysis // fall 2023

Li, Peter, Geometric Analysis , Cambridge University Press, 2012 (ISBN: 978-1-107-02064-1) — free e-book through the Cornell Math Library

MATH 7280 - Topics in Dynamical Systems: Mathematical Biology // fall 2023

Murray, J. D., Mathematical Biology I, 3rd edition , Springer 2002 (ISBN: 978-1-4757-7709-3) — free e-book through the Cornell Math Library

Murray, J. D., Mathematical Biology II: Spatial Models and Biomedical Applications, 3rd edition , Springer, 2002 (ISBN: 978-1-4757-7870-0) — free e-book through the Cornell Math Library

MATH 7510 - Berstein Seminar in Topology: 4-Manifolds // fall 2023

Gompf and Stipsicz, 4-Manifolds and Kirby Calculus , American Mathematical Society, 1999 (ISBN: 978-0-8218-0994-5) — free e-book through the Cornell Math Library

MATH 7570 - Topics in Topology: Category Theory // fall 2023

Riehl, Emily, Category Theory in Context , Dover Publications, 2016 (ISBN: 978-0-486--80903-8)

MATH 7670 - Topics in Algebraic Geometry  // spring 2023

Voisin, Claire, Hodge Theory and Complex Algebraic Geometry I , Cambridge University Press, 2002 (ISBN: 978-0-521-80260-4) — free e-book through the Cornell Math Library

Voisin, Claire, Hodge Theory and Complex Algebraic Geometry II , Cambridge University Press, 2002 (ISBN: 978-0-521-80283-3) — free e-book through the Cornell Math Library

MATH 7720 - Topics in Stochastic Processes  // spring 2023

Yadin, Ariel, Harmonic Functions and Random Walks on Groups (book in preparation).

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All textbooks available at:

MATTHEWS JOHNS HOPKINS MEDICAL BOOK CENTER 1830 East Monument Street Baltimore, MD 21205-2114 410-955-3931 1-800-266-5725

Epidemiologic Inference in Public Health I (340.721.89)

Required: Gordis Epidemiology (6th edition) by David Celentano, Moyses Szklo (2018). Elsevier (approx. cost $49.99) An electronic version of the textbook is available free of charge to JHU students at:   https://catalyst.library.jhu.edu/catalog/bib_7477802  There is a separate website for the book that is maintained by the publisher and may be useful, but access to this website requires purchase of the book.

Statistical Reasoning in Public Health I (140.611.11)

Recommended: Practical Statistics for Medical Research by D.G. Altman (1991). Chapman and Hall (approx. cost $99.95) Recommended: Intuitive Biostatistics by  Harvey Motulsky (2017) Oxford

Statistical Reasoning in Public Health II (140.612.11)

Recommended:  Fundamentals of Biostatistics  by  Bernard Rosner (2006)  Duxbury Press Recommended: Practical Statistics for Medical Research by D.G. Altman (1991). Chapman and Hall (approx. cost $99.95) Recommended: Intuitive Biostatistics by  Harvey Motulsky (2017) Oxford

Nutritional Epidemiology (340.650.11)

Recommended: Nutritional Epidemiology (2nd edition) by W.C. Willett (1998). Oxford University Press ( approx. cost $69.95)

Infectious Disease Epidemiology (340.668.11)

Required: Infectious Disease Epidemiology: Theory and Practice (3rd Edition) (2013). Edited by Kenrad E. Nelson and Carolyn Masters. Williams, Jones and Bartlett Publishers (approx. cost $163.95)

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Qualifying Requirements prior to Fall 2019

Qualifying exams.

Doctoral students are required to pass two qualifying exams.

• Comprehensive theory exam. This exam covers probability and theoretical statistics at the level of a graduate textbook such as "Statistical Inference" by Casella and Berger, used by Stats 510/511.  The comprehensive exam is offered twice a year, in late August and in late May. Students with advanced preparation may take this exam at the start of their first year. Two attempts are allowed, and the attempt at the start of the first year does not count towards this maximum of two.  All students need to pass this exam within 12 months of enrolling in the program unless an exception is approved by the PhD Program Director.
• Applied statistics exam. This exam tests modeling and data analysis skills and is roughly based on Stats 600/601. It is given as a 3-day take-home exam once a year in late May. Two attempts are allowed. All students need to pass this exam within two years of enrolling in the program unless an exception is approved by the PhD Program Director.

Program Requirements prior to Fall 2020

The Ph.D. in Statistics is flexible and allows students to pursue a variety of directions, ranging from statistical methodology and interdisciplinary research to theoretical statistics and probability theory. Students typically start the Ph.D. program by taking courses and gradually transition to research that will ultimately lead to their dissertation, the most important component of the Ph.D. program. The major requirements of the Ph.D. program are coursework, qualifying exams, advancement to candidacy, and dissertation. 

Required Courses

The core PhD curriculum consists of four course sequences, offered annually:

• Applied Statistics  — STATS 600 and 601
• Theoretical Statistics  — STATS 610 and 611
• Probability  — STATS 620 and 621
• Computational Methods for Statistics  — STATS 507 and STATS 606 ( prior to Fall 2019: STATS 607 I and II, 608 I and II )

Stats 600, 601, 610, 611, 620, and 621 are semester-long courses, and Stats 607 I and II, 608 I and II are half-semester modules. Any combination of two half-semester modules in the 607/608 sequence is equivalent to one course. All doctoral students must take at least 6 out of 8 required courses, with at least one course selected from each of the four sequences. A B+ average or higher in the six selected courses is required.

In addition, all students are required to complete two professional development seminar courses:

• STATS 810 , which covers research ethics and introduction to research tools. Must be taken in the first semester in the program.
• STATS 811 , which focuses on technical writing and presentation skills. Students are strongly advised to complete this course as soon as they have a writing project on which to work, such as a prelim proposal or a manuscript draft. Most students take this course in their second or third year. This course is required for graduation but not for advancing to candidacy.   

First Year Course Placement

Our Ph.D. program admits students with diverse academic backgrounds. All PhD students take Stats 600/601 (the PhD level applied statistics sequence) in their first year. Students with less mathematical backgrounds typically take Stats 510/511 (the Master’s level probability and theoretical statistics) in the first year and PhD-level theory courses (610/611, 620/621) in their second year. Students who wish to take 600-level theory courses in their first year should take the Theory QR exam offered just before the fall semester of their first year. Based on the results, they will either be approved to go on to the 600-level courses, or advised to take Stats 510/511. Passing the theory QR exam automatically places a student in 600-level courses, but one may also score high enough to place in 600-level courses without clearing the theory QR. In all cases, the PhD Program Director will help students choose their individual path through the required courses.

Qualifying Requirements

These requirements apply to students admitted in Fall 2019 and later. Students admitted in Fall 2018 can choose between the  old requirements  and the new requirements.  

All doctoral students need to satisfy the Applied and Theoretical Statistics qualifying requirements (QR).

• Applied statistics QR . This requirement is satisfied by passing a modeling and data analysis exam, roughly based on Stats 600/601. It is given as a 3-day take-home exam once a year in May. Two attempts are allowed. All students need to pass this exam within two years of enrolling in the program unless an exception is approved by the PhD Program Director.
• Theoretical statistics QR . This requirement may be satisfied by either excellent performance in certain courses (described below) or by passing the statistical theory exam offered once a year in late August. The exam covers probability and theoretical statistics at the level of a graduate textbook such as "Statistical Inference" by Casella and Berger, used by Stats 510/511. All PhD students need to satisfy the theoretical statistics QR by the beginning of their second year in the program unless an exception is approved by the PhD Program Director. A well-prepared student can opt to take this exam just before the start of their first year; if they do not pass, this attempt does not count. Whether they attempt this exam before the first year or not, all students can either qualify for an exemption based on course grades (see below) at the end of their first year, or take the exam in August just before the start of their second year. No further attempts are allowed.

A student can be exempt from taking the theoretical statistics QR exam based on coursework. To qualify for an exemption, the student can use their grades from two courses taken in their first year. One of the courses must be either Stats 510, 620, or 621 and the other course must be either Stats 511, 610, or 611. To qualify for an exemption, the average grade from the two chosen courses must be at least 3.65, and if at least one 500-level course is used, then the average must be at least 3.85. This is based on the conversion of letter grades to GPA points as follows: B- = 2.7, B = 3.0, B+ = 3.3, A- = 3.7, A = 4.0, A+ = 4.0.

Here are some examples of courses and grades that would qualify for an exemption:

• STATS 510 (A) and 511 (A-)
• STATS 510 (A) and 611 (A-)
• STATS 621 (A-) and 610 (A-)
• STATS 621 (B+) and 610 (A)

Advancing to Candidacy

Students who have passed the qualifying exams are expected to find a faculty advisor and start research leading to their dissertation proposal. The PhD Program Director and the faculty mentor assigned to each first year student can assist with finding a faculty advisor. Students are expected to submit a dissertation proposal and advance to candidacy within three semesters from passing the qualifying exams. Requirements for advancing to candidacy are:

• At least 18 credit hours of graduate course work , including at least 6 out of the required 8 core courses and Stats 810. A B+ average in the selected 6 core courses is required. Stats 808/809/818/819 (Department Seminar), Stats 990 (Dissertation Research) and similar non-graded courses do not count towards the credit requirement.
• At least 4 credit hours of cognates , which are 400- and higher-level courses from outside the Statistics department. All cognate course selections must be approved by the PhD Program Director.  
• Writing a dissertation proposal and passing the oral preliminary exam  which consists of presenting the proposal to the student's preliminary thesis committee.

A dissertation proposal should identify an interesting research problem, provide motivation for studying it, review the relevant literature, propose an approach for solving the problem​, and present at least some preliminary results​. The written proposal must be submitted to the preliminary thesis committee and the graduate coordinator a​head of time (one week minimum, two weeks recommended)​ and then presented in the oral preliminary exam. The preliminary thesis committee is chaired by the faculty advisor and must include at least two more faculty members, at least one of them from Statistics. ​​The faculty on the preliminary thesis committee typically continue t​o serve ​on ​the doctoral thesis committee​​, but changes are allowed.  Please see Rackham rules on thesis committees for more information.  

At the oral preliminary exam, the committee will ask questions about the proposal and the relevant background and either elect to accept the proposal as both substantial and feasible, or ask for specific revisions, or decline the proposal. The unanimous approval of the proposal by the committee is necessary for the student to advance to candidacy.

Additional Course Requirements

Students must take at least three additional PhD level semester-long courses or equivalent in half-semester modules. This requirement can be fulfilled with additional courses from the core sequences, advanced PhD courses, or topics courses. Stats 810, 811, and 750 (independent reading) do not count towards this requirement. While these additional courses are not required for advancement to candidacy, it is expected that students take at least some of them before advancing to candidacy. Taking courses after advancement to candidacy may require careful planning as candidates are allowed to take only one course per semester without an increase in tuition.

In addition, all PhD students are expected to register for Stats 808/809/818/819 (Department Seminar) every semester and attend the seminar regularly. Candidates registered for another course do not have to register for the department seminar, but are still expected to attend.

Exceptions to the above requirements may be granted by the PhD Program Director .

Annual Progress Reports

Each candidate is required to meet with the members of their thesis committee annually. This could be in the form of either giving a short presentation on their research progress to the thesis committee as a group, or meeting with committee members individually.

Each committee member should complete a  Thesis Committee Member Report  and return it to the student. The student should share the completed Thesis Committee Member Reports with both the PhD Program Coordinator and their advisor.

All meetings with the committee members should take place by  April 15.

Following the meetings, the student and the advisor should complete the  Annual PhD Candidate Self-Evaluation and Feedback Form . The advisor should review the committee members’ Thesis Committee Member Reports and take them into account when completing the advisor’s portion. The completed Annual PhD Candidate Self-Evaluation and Advisor Feedback Form must be submitted to the PhD Program Coordinator by  May 31. The completed form will be saved with the department, and a copy will be shared with the student.

Dissertation and Defense

Each doctoral student is expected to write a dissertation that makes a substantial and original contribution to statistics or a closely related field. This is the most important element of the doctoral program. After advancing to candidacy, students are expected to focus on their thesis research under the supervision of the thesis advisor and the doctoral committee. The composition of the doctoral committee must follow the Rackham's  guidelines for dissertation committee service . The written dissertation is submitted to the committee for evaluation and presented in an oral defense open to the public.

Rackham Requirements

The  Rackham Graduate School  imposes some additional requirements concerning residency, fees, and time limits. Students are expected to know and comply with these requirements. 

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Challenges to library books continue at record pace in 2023, American Library Association reports

FILE - Amanda Darrow, director of youth, family and education programs at the Utah Pride Center, poses with books that have been the subject of complaints from parents on Dec. 16, 2021, in Salt Lake City. The nationwide surge in book bannings continues. The American Library Association reported Wednesday, Sept. 20, 2023, that challenges to books in schools and public libraries will likely reach record highs in 2023, topping what had been a record pace in 2022. (AP Photo/Rick Bowmer, File)

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NEW YORK (AP) — Book bans and attempted bans continue to hit record highs , according to the American Library Association . And the efforts now extend as much to public libraries as school-based libraries.

Through the first eight months of 2023, the ALA tracked 695 challenges to library materials and services, compared to 681 during the same time period last year, and a 20% jump in the number of “unique titles” involved to 1,915. School libraries had long been the predominant target, but in 2023 reports have been near-equally divided between schools and libraries open to the general public, the ALA announced Wednesday.

“The irony is that you had some censors who said that those who didn’t want books pulled from schools could just go to the public libraries,”’ says Deborah Caldwell-Stone, who directs the association’s Office for Intellectual Freedom.

The ALA defines a challenge as a “formal, written complaint filed with a library or school requesting that materials be removed because of content or appropriateness.”

In 2019, the last pre-pandemic year, the association recorded just 377 challenges, involving 566 titles. The numbers fell in 2020, when many libraries were closed, but have since risen to the most in the association’s 20-plus year history of compiling data. Because the totals are based on media accounts and reports submitted by librarians, the ALA regards its numbers as snapshots, with many incidents left unrecorded.

Continuing a trend over the past two years, the challenges are increasingly directed against multiple titles. In 2023, complaints about 100 or more works were recorded by the ALA in 11 states, compared to six last year and none in 2021. The most sweeping challenges often originate with such conservative organizations as Moms for Liberty , which has organized banning efforts nationwide and called for more parental control over books available to children.

“There used to be a roughly one-to-one ratio, where a parent would complain about an individual book, like in the days when many were objecting to Harry Potter,” Caldwell-Stone says. “Now you have people turning up at meetings and asking that 100 titles be removed.”

The ALA released its numbers in advance of its annual banned books week, Oct. 1-7, when libraries highlight challenged works. Earlier this year, the association issued its annual top 10 list of the books most objected to in 2022, many of them featuring racial and/or LGBTQ themes. Maia Kobabe’s “Gender Queer” topped the list, followed by George Johnson’s “All Boys Aren’t Blue” and Nobel laureate Toni Morrison’s “The Bluest Eye.”

Attacks against teachers and librarians have been ongoing in 2023.

At Chapin High School in South Carolina, some students alleged that a teacher made them feel “ashamed to be Caucasian” for assigning Ta-Nehisi Coates’ “Between the World and Me,” an open letter to his son about police violence against Black people that won the National Book Award in 2015. The school removed the book from the syllabus.

In Fort Royal, Virginia, the county board of supervisors is planning to drastically cut funding for the Samuels Public Library in response to conservative complaints about books with gay, lesbian and transgender characters. Iowa Gov. Kim Reynolds signed into law a bill which calls for books depicting sex acts to be removed from school libraries.

Some attacks have affected the library association itself. The ALA’s opposition to bannings has led some communities to withdraw their membership, including Campbell County in Wyoming and a local library in Midland, Texas. Missouri officials announced the state would be leaving the ALA at a time when recent laws limited access for young people to books considered inappropriate for their age.

“I think this trend is going to continue,” Caldwell-Stone says, “at least for as long these groups want to go after whole categories of books.”