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Zbl 1051.65007
Neal, Radford M.
(Chen, Ming-Hui; Schmeiser, Bruce W.; Downs, Oliver B.; Mira, Antonietta; Roberts, Gareth O.; Skilling, John; MacKay, David J. C.; Walkers, S. G.)
Slice sampling. (With discussions and rejoinder). (English)
[J] Ann. Stat. 31, No. 3, 705-767 (2003). ISSN 0090-5364

The author describes a class of slice sampling methods that can be applied to a wide variety of distributions. Section~2 summarizes general-purpose Markov chain sampling methods as the Gibbs sampling, the adaptive rejection sampling, the adaptive rejection Metropolis sampling etc. \par Section~3 presents the basic ideas of a slice sampling and thoroughly discusses different predecessors more or less connected to it. The principal message of the paper is concentrated in chapters 4--7. At first, simple variable slice samplings methods are described. Then the author concentrates on multivariate slice sampling methods and reflective slice sampling. An example forms the final section. \par I liked the paper and I must say that despite it is a paper for Annals of Statistics, the author really concentrates on the ideas and not on the formal proofs as is typical for this journal. I am sure that everybody who want to get an idea of what is slice sampling will be satisfied. \par The paper is complemented by an interesting discussion prepared by Ming-Hui Chen, B. W. Schmeiser, O. B. Downs, A. Mira, G. O. Roberts, J. Skilling, D. J. C. MacKey and G. S. Walker.
[Jaromir Antoch (Praha)]

MSC 2000:: *65C60 Computational problems in statistics
65C05 Monte Carlo methods
62D05 Statistical sampling theory
65C40 Computational Markov chains

Keywords: slice sampling; Markov chain Monte Carlo method; adaptive methods; Gibbs sampling; Metropolis algorithm; overrelaxation; dynamical methods; reflective slice sampling

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