This book provides a compact self-contained introduction to the theory and application of Bayesian statistical methods. The book is accessible to readers having a basic familiarity with probability, yet allows more advanced readers to quickly grasp the principles underlying Bayesian theory and methods. The examples and computer code allow the reader to understand and implement basic Bayesian data analyses using standard statistical models and to extend the standard models to specialized data analysis situations. The book begins with fundamental notions such as probability, exchangeability and Bayes' rule, and ends with modern topics such as variable selection in regression, generalized linear mixed effects models, and semiparametric copula estimation. Numerous examples from the social, biological and physical sciences show how to implement these methodologies in practice. onte Carlo summaries of posterior distributions play an important role in Bayesian data analysis. The open-source R statistical computing environment provides sufficient functionality to make Monte Carlo estimation very easy for a large number of statistical models and example R-code is provided throughout the text. Much of the example code can be run as is' in R, and essentially all of it can be run after downloading the relevant datasets from the companion website for this book. TOC:Introduction and examples.- Belief, probability and exchangeability.- One parameter models.- Monte Carlo approximation.- The normal model.- Posterior approximation with the Gibbs sampler.- The multivariate normal model.- Group comparisons and hierarchical modeling.- Linear regression.- Nonconjugate priors and the Metropolis-Hastings algorithm.- Linear and generalized linear mixed effects models.- Latent variable methods for ordinal data. This compact, self-contained introduction to the theory and application of Bayesian statistical methods is accessible to those with a basic familiarity with probability, yet allows advanced readers to grasp the principles underlying Bayesian theory and method.