Bayesian statistics?! Once an obscure term outside specialized industry and research circles, Bayesian methods are enjoying a renaissance. The title of this book speaks to what all the fuss is about: Bayes Rules! Bayesian methods provide a powerful alternative to the frequentist methods that are ingrained in the standard statistics curriculum. Though frequentist and Bayesian methods share a common goal – learning from data – the Bayesian approach to this goal is gaining popularity for many reasons: (1) Bayesian methods allow us to interpret new data in light of prior information, formally weaving both into a set of updated information; (2) relative to the confidence intervals and p-values utilized in frequentist analyses, Bayesian results are easier to interpret; (3) Bayesian methods can shine in settings where frequentist “likelihood” methods break down; and (4) the computational tools required for applying Bayesian techniques are increasingly accessible. Unfortunately, the popularity of Bayesian statistics has outpaced the curricular resources needed to support it. To this end, the primary goal of Bayes Rules! is to make modern Bayesian thinking, modeling, and computing accessible to a broader audience.


Bayes Rules! brings the power of Bayes to advanced undergraduate students and comparably trained practitioners. Accordingly, the book is neither written at the graduate level nor is it meant to be a first introduction to the field of statistics. At minimum, 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. But wait! Please don’t go away if you don’t check off all of these boxes. We provide all R code and enough probability review so that 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. Further, though certain calculus concepts are important in Bayesian analysis (thus the book), calculus derivations are not. The latter are limited to the simple model settings in early chapters and easily skippable.

Getting set up

Once you’re ready to dive into Bayes Rules!, take the following steps to get set up. First, download the most recent versions of the following software:

Next, install the following packages within RStudio:

  • Install the rstan package by carefully following the directions at

  • Install a set of data wrangling and Bayesian packages by typing the following in your console.

    install.packages(c("bayesrules", "tidyverse", "janitor", "rstanarm",
                       "bayesplot", "tidybayes", "broom.mixed", "modelr",
                       "e1071", "forcats"), 
                     dependencies = TRUE)
  • The bayesrules package contains some datasets and functions we’ve built explicitly for the Bayes Rules! book. Several of the datasets in this package have been extracted from larger sources, using non-random methods to obtain subsets that match our pedagogical goals. These potentially biased datasets should not be used for rigorous research purposes. Should this be your goal, please see the relevant data help file to identify the original, complete data source.

Finally, check out This website contains more background information about the book as well as supporting resources that will continue to grow over time.

Accessibility and inclusion

We are dedicated to providing an inclusive and accessible Bayesian resource. We are continuing to learn, and shared our current efforts at All the figures in the online version book are supported by alternate text and should be able accessible to readers using a screen-reader.

Contact us

As you read and interact with Bayes Rules!, please feel free to drop us a note through the form posted on our website: We’re especially curious to know if: you have any ideas for increasing the accessibility and inclusion of this book; you notice any errors or typos; and there’s anything you’d like to see in future versions. When we revise the text, we will occasionally check in with this form to help guide that process.


First and foremost, we’d like to thank the students we’ve worked with at Augsburg University, Carleton College, Denison University, Macalester College, Smith College, and the University of California, Irvine. Their feedback, insights, and example inspired a high bar for the type of book we wanted to put out into the world. Beyond our students, we received valuable feedback from numerous colleagues in the Statistics and Data Science community. Special thanks to: James Albert, Virgilio Gómez Rubio, Amy Herring, David Hitchcock, Nick Horton, Yue Jiang, and Paul Roback. And to our supportive editor, David Grubbs. He certainly made this first adventure in book publishing more chill and enjoyable than we expected.

Beyond those above, Alicia would especially like to thank the following:

  • John Kim, Martha Skold, the Johnsons, and Minneapolis friends for their support, even on the dreaded “writing brain” days.
  • Galin Jones for his inviting enthusiasm about statistical computation.
  • The STAT 454 students at Macalester College for their inspiring curiosity and the STAT 454 teaching assistants for supporting their peers in learning about Bayes (Zuofu Huang, Sebastian Coll, Connie Zhang).
  • Colleagues in the Department of Mathematics, Statistics, and Computer Science at Macalester College – you are a humane, fun, and reflective crew.

Miles would especially like to thank the following:

  • Francesca Giardine, Sarah Glidden, and Elaona Lemoto for testing out half-formed exercises, gently pointing out errors, and giving excellent suggestions. It was an honor to get to work with you at this early stage of your statistics careers.
  • The Smith College SDS 320 students from spring 2019 and the SDS 390 students from fall 2020 (especially Audrey Bretin, Dianne Caravela, Marlene Jackson, and Hannah Snell who provided helpful feedback on Chapter 8).
  • His colleagues from Smith College SDS.
  • The WSDS conference for being the starting point for many friendships and collaborations, including this book.
  • His family, Bea Capistrant, Ethan Suniewick, Malkah Bird, Henry Schneiderman, Christopher Tradowsky, Ross Elfline, Jon Knapp, and Alex Callendar.

Mine would especially like to thank the following:

  • Morteza Khakshoor, family, and friends who are far only in distance, for their love, support, and understanding.
  • The late Binnaz Melin for being supportive of her career from a young age.
  • Students of STATS 115 at UC Irvine who always are the best part of teaching Bayesian statistics.
  • Her colleagues in the Department of Statistics at UC Irvine.
  • All those in the statistics and R community who are supportive of, and kind towards, others, especially newcomers.

Finally, we would all like to thank each other for recognizing the importance of humor, empathy, and gratitude to effective collaboration. Deciding to tackle this project before we really knew one another was a pretty great gamble. It’s been fun!