An engaging, sophisticated, and fun introduction to the field of Bayesian statistics, Bayes Rules!: An Introduction to Applied Bayesian Modeling brings the power of modern Bayesian thinking, modeling, and computing to a broad audience. In particular, the book is an ideal resource for advanced undergraduate statistics students and practitioners with comparable experience. the book assumes that readers are familiar with the content covered in a typical undergraduate-level introductory statistics course. Readers will also, ideally, have some experience with undergraduate-level probability, calculus, and the R statistical software. Readers without this background will still be able to follow along so long as they
are eager to pick up these tools on the fly as all R code is provided.Bayes Rules! empowers readers to weave Bayesian approaches into their everyday practice. Discussions and applications are data driven. A natural progression from fundamental to multivariable, hierarchical models emphasizes a practical and generalizable model building process. The evaluation of these Bayesian models reflects the fact that a data analysis does not exist in a vacuum.
• Utilizes data-driven examples and exercises.
• Emphasizes the iterative model building and evaluation process.
• Surveys an interconnected range of multivariable regression and classification models.
• Presents fundamental Markov chain Monte Carlo simulation.
• Integrates R code, including RStan modeling tools and the bayesrules package.
• Encourages readers to tap into their intuition and learn by doing.
• Provides a friendly and inclusive introduction to technical Bayesian concepts.
• Supports Bayesian applications with foundational Bayesian theory.
Table of Contents
Chapter 1 The Big (Bayesian) Picture
Chapter 2 Bayes’ Rule
Chapter 3 The Beta-Binomial Bayesian Model
Chapter 4 Balance and Sequentiality in Bayesian Analyses
Chapter 5 Conjugate Families Chapter 6 Approximating the Posterior
Chapter 7 MCMC Under the Hood
Chapter 8 Posterior Inference and Prediction
Chapter 9 Simple Normal Regression
Chapter 10 Evaluating Regression Models
Chapter 11 Extending the Normal Regression Model
Chapter 12 Poisson and Negative Binomial Regression
Chapter 13 Logistic Regression
Chapter 14 Naive Bayes Classification
Chapter 15 Hierarchical Models are Exciting
Chapter 16 (Normal) Hierarchical Models Without Predictors
Chapter 17 (Normal) Hierarchical Models With Predictors
Chapter 18 Non-Normal Hierarchical Regression & Classification
Chapter 19 Adding More Layers Bibliography Index
Alicia Johnson is an Associate Professor of Statistics at Macalester College in Saint Paul, Minnesota. She enjoys exploring and connecting students to Bayesian analysis, computational statistics, and the power of data in contributing to this shared world of ours.
Miles Ott is a Senior Data Scientist at The Janssen Pharmaceutical Companies of Johnson & Johnson. Prior to his current position, he taught at Carleton College, Augsburg University, and Smith College. He is interested in biostatistics, LGBTQ+ health research, analysis of social network data, and statistics/data science education. He blogs at milesott.com and tweets about statistics, gardening, and his dogs on Twitter.
Mine Dogucu is an Assistant Professor of Teaching in the Department of Statistics at University of California Irvine. She spends majority of her time thinking about what to teach, how to teach it, and what tools to use while teaching. She likes intersectional feminism, cats, and R Ladies. She tweets about statistics and data science education on Twitter.
"As an alternative to “technical derivations” Bayes Rules! centres on intuition and simulation (yay!) via its bayesrule R package. Itself relying on rstan. Learning from example (as R code is always provided), the book proceeds through conjugate priors, MCMC (Metropolis-Hasting) methods, regression models, and hierarchical regression models. Quite impressive given the limited prerequisites set by the authors. (I appreciated the representations of the prior-likelihood-posterior, especially in the sequential case.)"
-Christian Robert, University of Warwick, UK, Xi'an's OG
"A thoughtful and entertaining book, and a great way to get started with Bayesian analysis."
-Andrew Gelman, Columbia University
"I like the book. It’s a comprehensive introduction to Bayesian modelling, including several applied bits of code to help the reader through the complex mathematical details … I think [it] is a solid addition to the literature."
-Gianluca Baio, University College, London
"Great work, wow! Thanks so much for doing this! The exercises are fresh and innovative, and I will be working several of them into my courses. I like the focus/level in appealing to introductory students. The examples are modern, and even many frequentist intro books ignore important topics (like the great p-value debate) that the authors address. The focus on simulation for understanding is excellent."
– Amy Herring, Duke University
"I congratulate and commend the authors for writing a textbook that makes statistics come alive. I sincerely believe that a generation of students will cite this book as inspiration for their use of – and love for – Bayesian statistics. The narrative holds the reader’s attention and flows naturally – almost conversationally. Put simply, this is perhaps the most engaging introductory statistics textbook I have ever read. The small but frequent "Quiz Yourself" sections were effective in reinforcing material in low stakes scenarios, and homework problems were clearly developed with great care, providing a mix of conceptual and applied methodological exercises to cement student understanding. I thoroughly enjoyed reviewing this book; it was a true delight to read and is a natural choice for an introductory undergraduate course in applied Bayesian statistics."
– Yue Jiang, Duke University
"It is a lot of fun to read! It’s clearly targeted at an undergraduate audience, and the writing style is geared toward less advanced undergraduates … It has a lot of examples that would appeal to undergraduate students. It does cover quite a lot of methods and approaches. It’s quite comprehensive for a book of its level." –
David Hitchcock, University of South Carolina
"It is a nice, well-written text on Bayesian modeling with an emphasis on regression and multilevel modeling. It can be used for a one-semester or two-semester course in Bayesian statistics at the undergraduate or master’s level. It introduces the methods in the context of interesting datasets and the computational methods are current using the popular MCMC Stan software. It appears to have a sufficient number of exercises and self-study quizzes that make it useful for self-study or the classroom."
– Jim Albert, Bowling Green University
"Books on Bayesian modeling that I’ve seen have been flawed in crucial ways that prevented the reader from truly becoming a knowledgeable practitioner of Bayesian methods – the examples were only elementary and unrealistic, the presentation of software was too black box-ish, or the mathematical and computational details ramped up way too quickly. This is the first book I’ve seen that hits the sweet spot – starting with basic building blocks but progressing eventually to realistic case studies, development of intuition behind the methods, and appropriate scaffolding of ideas. Amazing work by the authors!"
– Paul Roback, St. Olaf College
"I think the authors do a nice job with examples to illustrate concepts and help the readers (students) develop intuition about Bayesian inference. Chapters include questions that ask the reader to consider likely answers to inferential questions based on the information provided. The formal Bayesian inferences follow the questions, with enough explanation to help the reader determine what thought processes might have led to the correct Bayesian approach to answering the question. A goal is to teach and to reinforce the reader’s intuition along the way. Many of the examples relate to contemporary media and social matters. Such examples help."
-Gary Rosner, Johns Hopkins University
"The authors provide a compelling, integrated, accessible, and non-religious introduction to statistical modeling using a Bayesian approach. They outline a principled approach that features computational implementations and model assessment with ethical implications interwoven throughout. Students and instructors will find the conceptual and computational exercises to be fresh and engaging."
-Nick Horton, Amherst College
"The [book] provides a very nice introduction to Bayesian inference and modeling. The authors describe these topics using a wealth of different datasets and provide a number of exercises at the end of every chapter. I have particularly enjoyed how each chapter is structured: the authors present a problem or dataset and they develop the chapter by telling a story that involves the dataset introduced and by addressing the problem using Bayesian inference and modeling. There are also plenty of thought-provoking questions and exercises throughout the book. Furthermore, the authors also discuss different ethical issues on statistical modeling and inference. ...I really enjoyed reading it."
-Virgilio Gomez-Rubio, Universidad de Castilla-la Mancha