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Advanced Markov chain Monte Carlo methods. Learning from past samples. (English) Zbl 1209.62009
Wiley Series in Probability and Statistics. Chichester: John Wiley & Sons (ISBN 978-0-470-74826-8/hbk; 978-0-470-66972-3/ebook). xix, 357 p. (2010).
This book surveys sampling algorithms for iterative simulations of random experiments under the scope of the Markov Chain Monte Carlo (MCMC) approach. Particular emphasis is thereby laid on techniques which are immune to the “local trap” problem and circumvent the “intractable integral” problem by utilizing information that is contained in past samples.
Seven chapters (2–8) divide the respective material into subcategories of modern MCMC methods. This facilitates the usage of the book for teaching a Master’s or Ph. D. course, especially since each chapter is accompanied by exercises. The preparatory Chapter 1 provides a profound introduction to necessary elementary results from probability theory and mathematical statistics which is also of independent value. Sampling techniques are treated both mathematically and algorithmically. In particular, R code snippets are provided on various occasions.
Researchers working in the field of applied statistics will profit from this easy-to-access presentation. Further illustration is done by discussing interesting examples and relevant applications. The valuable reference list includes technical reports which are hard to find by searching in public data bases.

MSC:
62D99 Statistical sampling theory and related topics
62-02 Research exposition (monographs, survey articles) pertaining to statistics
65C40 Numerical analysis or methods applied to Markov chains
65C05 Monte Carlo methods
60J22 Computational methods in Markov chains
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