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Monte Carlo Methods in Bayesian Computation

By: Ming-Hui Chen, Qi-Man Shao and Joseph G Ibrahim

408 pages, 20 illus


Hardback | Dec 2000 | #106861 | ISBN: 0387989358
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NHBS Price: £119.99 $158/€137 approx

About this book

This book examines advanced Bayesian computational methods. It presents methods for sampling from posterior distributions and discusses how to compute posterior quantities of interest using Markov chain Monte Carlo (MCMC) samples. This book examines each of these issues in detail and heavily focuses on computing various posterior quantities of interest from a given MCMC sample. Several topics are addressed, including techniques for MCMC sampling, Monte Carlo methods for estimation of posterior quantities, improving simulation accuracy, marginal posterior density estimation, estimation of normalizing constants, constrained parameter problems, highest posterior density interval calculations, computation of posterior modes, and posterior computations for proportional hazards models and Dirichlet process models. The authors also discuss computions involving model comparisons, including both nested and non-nested models, marginal likelihood methods, ratios of normalizing constants, Bayes factors, the Savage-Dickey density ratio, Stochastic Search Variable Selection, Bayesian Model Averaging, the reverse jump algorithm, and model adequacy using predictive and latent residual approaches. The book presents an equal mixture of theory and applications involving real data. The book is intended as a graduate textbook or a reference book for a one semester course at the advanced masters or Ph.D. level. It would also serve as a useful reference book for applied or theoretical researchers as well as practitioners. Ming-Hui Chen is Associate Professor of Mathematical Sciences at Worcester Polytechnic Institute, Qu-Man Shao is Assistant Professor of Mathematics at the University of Oregon. Joseph G. Ibrahim is Associate Professor of Biostatistics at the Harvard School of Public Health and Dana-Farber Cancer Institute.

This book combines the theory topics with good computer and application examples from the field of food science, agriculture, cancer and others. The volume will provide an excellent research resource for statisticians with an interest in computer intensive methods for modelling with different sorts of prior information. A.V. Tsukanov in "Short Book Reviews", Vol. 20/3, December 2000


Introduction.- Markov Chain Monte Carlo Sampling.- Basic Monte Carlo Methods for Estimating Posterior Quantities.- Estimating Marginal Posterior Densities.- Estimating Ratios of Normalizing Constants.- Monte Carlo Methods for Constrained Parameter Problems.- Computing Bayesian Credible and HPD Intervals.- Bayesian Approaches for Comparing Non-Nested Models.- Bayesian Variable Section.- Other Topics.

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