UC Berkeley Statistics Grad Student Association Recommended Books

Recommended books by the UC Berkeley SGSA. Source.

Applied Statistics - Categorical Data

Categorical Data Analysis

Agresti

Well-written, go-to reference for all things involving categorical data.

Applied Statistics - Linear Models

Generalized Linear Models

McCullagh/Nelder

Theoretical take on GLMs. Does not have a lot of concrete data examples.

Statistical Models

Freedman

...Berkeley classic!

Linear Models With R

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.

Design of Comparative Experiments

Bailey

Classic, approachable text, [Available online.]

Applied Statistics - Machine Learning

The Elements of Statistical Learning

Hastie/Tibshirani/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. [Available online.]

Computer Age Statistical Inference: Algorithms, Evidence, and Data Science

Hastie/Efron

Pattern Recognition and Machine Learning

Bishop

Bayesian Reasoning and Machine Learning

Barber

[Available online.]

Probabilistic Graphical Models

Koller/Friedman

Theoretical Statistics

Theoretical Statistics: Topics for a Core Course

Keener

The primary text for Stat 210A. [Download from SpringerLink.]

Theory of Point Estimation

Lehmann/Casella

A good reference for Stat 210A.

Testing Statistical Hypotheses

Lehmann/Romano

A good reference for Stat 210A.

Empirical Processes in M-Estimation

van de Geer

Some students find this helpful to supplement the material in 210B.

Probability - Undergraduate Level

Probability

Pitman

What the majority of Berkeley undergraduates use to learn probability.

Introduction to Probability Theory

Hoel/Port/Stone

This text is more mathematically inclined than Pitman's, and more concise, but not as good at teaching probabilistic thinking.

Probability and Computing

Upfal/Mitzenmacher

What students in EECS use to learn about randomized algorithms and applied probability.

Probability - Measure Theoretic

Probability: Theory and Examples

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. [Available online.]

Foundations of Modern Probability

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

Billingsley

This text is often a useful supplement for students taking 205 who have not previously done measure theory.

Probability With Martingales

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.

Probability - 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

Revuz/Yor

Diffusions, Markov Processes and Martingales (Volumes 1 and 2)

Rogers/Williams

Brownian Motion and Stochastic Calculus

Karatzas/Shreve

Probability - Random Walk and Markov Chains

These are indispensable tools of probability. Some nice references are

Markov Chain and Mixing Times

Levin/Peres/Wilmer

[Available online.]

Markov Chains

Norris

Starting with elementary examples, this book gives very good hints on how to think about Markov Chains.

Continuous Time Markov Processes

Liggett

A theoretical perspective on this important topic in stochastic processes. The text uses Brownian motion as the motivating example.

Mathematics - Convex Optimization

Convex Optimization

Boyd/Vandenberghe

[Available online.]

Introductory Lectures on Convex Optimization

Nesterov

Mathematics - Linear Algebra

The Matrix Cookbook

Petersen/Pedersen

[Available online.]

Matrix Analysis

Horn/Johnson

Topics in Matrix Analysis

Horn/Johnson

Second book is more advanced than the first. Everything you need to know about matrix analysis.

Mathematics - Convex Analysis

A Course in Convexity

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.

Mathematics - Measure Theory

Real Analysis and Probability

Dudley

Very comprehensive.

Probability and Measure Theory

Ash

Nice and easy to digest. Good as companion for 205A.

Mathematics - Combinatorics

Enumerative Combinatorics Vol I and II

Stanley

There's also a course on combinatorics this semester in the math department called Math 249: Algebraic Combinatorics. Despite the scary "algebraic" prefix it's really fun. [Available online.]

Computational Biology

Statistical Methods in Bioinformatics

Ewens/Grant

Great overview of sequencing technology for the unacquainted.

Computational Genome Analysis: An Introduction

Deonier/Tavare/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

Durrett

Mathematical Population Genetics

Ewens

Computer Science - Numerical Analysis

Numerical Analysis

Burden/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.

Computer Science - Algorithms

Introduction to Algorithms

Cormen/Leiserson/Rivest/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

Kleinberg/Tardos