This book is an overview of the Bayesian approach to applying the most important inferential methods of statistical science. It is designed as a textbook for advanced undergraduate and master’s students in Data Science, Statistics, or Mathematics who are interested in learning about Bayesian statistics.

The reader should be familiar with calculus and should have taken a statistical inference Statistics course covering the basic rules of probability, probability distributions and expectations, as well as the fundamentals of the traditional, frequentist approach to statistics, including sampling distributions, likelihood functions, basic inferential methods such as point estimation, confidence intervals, significance tests, and linear regression models.

Key Features:

● Uses real world data examples and contains numerous exercises.

● Includes software appendices in R and Python.

● Offers slides, labs, and other materials on the book’s website.

Each chapter begins with a brief review of the primary frequentist methods for its topic before introducing corresponding Bayesian methods. This book presents some substantive theory as well as the methods, and is therefore intended for a reader who wishes to understand Bayesian methods rather than merely apply them. The focus is not just on presenting statistical methodologies but also on demonstrating how to implement them with modern software, emphasizing appropriate simulation methods.

1. Introduction to Bayesian Statistics 2. Bayesian Inference for Proportions 3. Bayesian Inference for Means 4. Bayesian Inference for Linear Models 5. Bayesian Inference for Generalized Linear Models 6. Bayesian MCMC Posterior Computation and Diagnostics 7. Choosing and Extending Bayesian Models Appendix A Using R for Bayesian Data Analysis Appendix Appendix B Using Python in Statistical Science Appendix C Solutions to Exercises (odd-numbered)