# Foreword

Even after decades of thinking about it, Bayes’ Rule never ceases to amaze me. How can one simple formula have such a wide variety of applications? You will encounter a vibrant sample of such applications in this book, ranging from weather prediction to LGBTQ+ anti-discrimination laws, and from who calls soda “pop” (or calls pop “soda”) to how to classify penguin species. Most importantly, careful study of this book will empower you to conduct thoughtful Bayesian analyses for the data and applications *you* care about.

Statistics and data science focus on using data to learn about the world and make predictions. The Bayesian approach gives a principled, powerful tool for obtaining probabilities and predictions about our unknown quantities of interest, given what we do know (the data). It gives easy-to-interpret results that directly quantify our uncertainties. Unfortunately, it is rarely taught in depth at the undergraduate level, perhaps out of concern that there would be too many scary-looking integrals to do or too much cryptic code to write.

*Bayes Rules!* shows that the Bayesian approach *is* in fact accessible to students and self-learners with basic statistics knowledge, even if they are not adept at calculus derivations or coding up fancy algorithms from scratch. The book achieves this with many reader-friendly features, such as clear explanations through words and pictures, quizzes to test your understanding, and the **bayesrules** R package that contains datasets and functions that facilitate trying out Bayesian methods.

Better yet, the accessibility is achieved through good pedagogy, not through giving a watered down, over-simplified look at the subject. For example, models called *hierarchical models* and an R package called **rstan** are introduced, with highly instructive examples showing how to apply these to interesting applications. Hierarchical models and **rstan** are among the state-of-the-art techniques used in modern Bayesian data analysis.

The Peter Parker principle from the Spider-Man comics says, “With great power comes great responsibility.” Likewise, the great power of statistics and data science comes with the great responsibility to consider the benefits and risks to society, the privacy rights of the participants in a study, the biases in a dataset and whether a proposed algorithm amplifies those biases, and other ethical issues. *Bayes Rules!* emphasizes *fairness* and *ethics* rather than ignoring these crucial issues.

Given that you read *Bayes Rules!* (actively – make sure to try the self-quizzes and practice with some exercises!), the probability is high that you will strengthen your statistical problem-solving skills while experiencing the joy of Bayesian thinking.

—*Joseph K. Blitzstein, Harvard University*