Understanding Computational Bayesian Statistics - Hardcover

Bolstad, William M.

Hardcover

ISBN 10: 0471270202 ISBN 13: 9780471270201

Publisher: Wiley–Blackwell, 2004

Synopsis

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.

About this title

Review

"I would recommend this book if you are interested in teaching an introductory in Bayesian statistics..."  (The American Statistician, February 2006)

"...a very useful undergraduate text presenting a novel approach to an introductory statistics course." (Biometrics, September 2005)

"I cannot think of a better book for teachers of introductory statistics who want a readable and pedagogically sound text to introduce Bayesian statistics." (Statistics in Medical Research, October 2005)

"...this book fills a gap for teaching elementary Bayesian statistics...it could easily serve as a self–learning text..." (Technometrics, May 2005)

[In a review comparing Bolstad with another book,] "I will keep both of these books on my shelf, but I expect that Bolstad will be the one most borrowed by my colleagues."(significance, December 2004)

"...does an excellent job of presenting Bayesian Statistics as a perfectly reasonable approach to elementary problems of statistics...I must heartily recommend this book..." (STATS: The Magazine for Students of Statistics, Fall 2004)

From the Back Cover

Traditionally, introductory statistics courses have been taught from a frequentist perspective. The recent upsurge in the use of Bayesian methods in applied statistical analysis highlights the need to expose students early on to the Bayes theorem, its advantages, and its applications. Based on the author s successful courses, Introduction to Bayesian Statistics introduces statistics from a Bayesian perspective in a way that is understandable to readers with a reasonable mathematics background.

Covering most of the same ground found in a typical statistics book but from a Bayesian perspective Introduction to Bayesian Statistics offers thorough, clearly–explained discussions of:

• Scientific data gathering, including the use of random sampling methods and randomized experiments to make inferences on cause–effect relationships
• The rules of probability, including joint, marginal, and conditional probability
• Discrete and continuous random variables
• Bayesian inferences for means and proportions compared with the corresponding frequentist ones
• The simple linear regression model analyzed in a Bayesian manner

To assist in the understanding of Bayesian statistics, this introduction provides readers with exercises (with selected answers); summaries of main points from each chapter; a calculus refresher, and a summary on the use of statistical tables; and R functions and Minitab macros for Bayesian analysis and Monte Carlo simulations (downloadable from the associated Web site)

Edition details

• Publisher: Wiley–Blackwell
• Publication date: 2004
• ISBN 10: 0471270202
• ISBN 13: 9780471270201
• Binding: Hardcover
• Language: English
• Number of pages: 376