Book description
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.
William M. Bolstad, PhD, is Senior Lecturer in the
Department of Statistics at The University of Waikato (New Zealand).
Dr. Bolstad's research interests include Bayesian statistics, MCMC
methods, recursive estimation techniques, multiprocess dynamic time
series models, and forecasting. He is the author of Introduction to
Bayesian Statistics, Second Edition, also published by Wiley.
