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.
Praise for Bayes Rules!: An Introduction to Applied Bayesian Modeling
“A thoughtful and entertaining book, and a great way to get started with Bayesian analysis.”
Andrew Gelman, Columbia University
“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 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. [It] is a natural choice for an introductory undergraduate course in applied Bayesian statistics."
Yue Jiang, Duke University
“This is by far the best book I’ve seen on how to (and how to teach students to) do Bayesian modeling and understand the underlying mathematics and computation. The authors build intuition and scaffold ideas expertly, using interesting real case studies, insightful graphics, and clear explanations. The scope of this book is vast – from basic building blocks to hierarchical modeling, but the authors’ thoughtful organization allows the reader to navigate this journey smoothly. And impressively, by the end of the book, one can run sophisticated Bayesian models and actually understand the whys, whats, and hows.”
Paul Roback, St. Olaf College
“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.”
Nicholas Horton, Amherst College