Understanding Computational Bayesian Statistics / Wiley Series in Computational Statistics (ePub)

A hands-on introduction to computational statistics from
a Bayesian point of view

Providing a solid grounding in statistics while uniquely
covering the topics from a Bayesian perspective, Understanding
Computational Bayesian Statistics successfully guides readers
through this new, cutting-edge approach. With its hands-on
treatment of the topic, the book shows how samples can be drawn
from the posterior distribution when the formula giving its shape
is all that is known, and how Bayesian inferences can be based on
these samples from the posterior. These ideas are illustrated on
common statistical models, including the multiple linear regression
model, the hierarchical mean model, the logistic regression model,
and the proportional hazards model.

The book begins with an outline of the similarities and
differences between Bayesian and the likelihood approaches to
statistics. Subsequent chapters present key techniques for using
computer software to draw Monte Carlo samples from the incompletely
known posterior distribution and performing the Bayesian inference
calculated from these samples. Topics of coverage include:

* Direct ways to draw a random sample from the posterior by
reshaping a random sample drawn from an easily sampled starting
distribution

* The distributions from the one-dimensional exponential
family

* Markov chains and their long-run behavior

* The Metropolis-Hastings algorithm

* Gibbs sampling algorithm and methods for speeding up
convergence

* Markov chain Monte Carlo sampling

Using numerous graphs and diagrams, the author emphasizes a
step-by-step approach to computational Bayesian statistics. At each
step, important aspects of application are detailed, such as how to
choose a prior for logistic regression model, the Poisson
regression model, and the proportional hazards model. A related Web
site houses R functions and Minitab macros for Bayesian analysis
and Monte Carlo simulations, and detailed appendices in the book
guide readers through the use of these software packages.

Understanding Computational Bayesian Statistics is an
excellent book for courses on computational statistics at the
upper-level undergraduate and graduate levels. It is also a
valuable reference for researchers and practitioners who use
computer programs to conduct statistical analyses of data and solve
problems in their everyday work.