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.
A complete solutions manual is available for instructors who adopt the
book in the Additional Resources section.
