Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors' research.
This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection.
The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book.
About the Authors
Jim Albert is a Distinguished University Professor of Statistics at Bowling Green State University. His research interests include Bayesian modeling and applications of statistical thinking in sports. He has authored or coauthored several books including
Ordinal Data Modeling, Bayesian Computation with R, and
Workshop Statistics: Discovery with Data, A Bayesian Approach.
Jingchen (Monika) Hu is an Assistant Professor of Mathematics and Statistics at Vassar College. She teaches an undergraduate-level Bayesian Statistics course at Vassar, which is shared online across several liberal arts colleges. Her research focuses on dealing with data privacy issues by releasing synthetic data.
Industry Reviews
"The book can be used by upper undergraduate and graduate students as well as researchers and practitioners in statistics and data science from all disciplines...A background of calculus is required for the reader but no experience in programming is needed. The writing style of the book is extremely reader friendly. It provides numerous illustrative examples, valuable resources, a rich collection of materials, and a memorable learning experience."
~Technometrics
"Over many years, I have wondered about the following: Should a first undergraduate course in statistics be a Bayesian course? After reading this book, I have come to the conclusion that the answer is...yes!... this is very well written textbook that can also be used as self-learning material for practitioners. It presents a clear, accessible, and entertaining account of the interplay of probability, computations, and statistical inference from the Bayesian perspective."
~ISCB News
