Perfect sampling from independent Metropolis-Hastings chains
type: Item
instance of: scholarly article
title: Perfect sampling from independent Metropolis-Hastings chains
zbMATH Open document ID: 0999.60068
DOI: 10.1016/S0378-3758(01)00243-9
published in: Journal of Statistical Planning and Inference
publication date: 2002-08-28T00:00:00Z
review text: The paper investigates the process of perfect sampling for independent Metropolis-Hastings (IMH) chains. The authors show that the IMH chain has certain stochastic monotonicity properties that enable a perfect sampling algorithm to be implemented, at least when the candidate is over-dispersed with respect to the target distribution. More precisely, one proves that, under certain conditions, the IMH chain has a minimal element and, furthermore, one can construct an upper process in this case. Thus IMH backward coupling is a viable way to derive perfect samples. The proposed IMH algorithm is proved to have an optimal geometric convergence rate, and it is illustrated on three examples. In the first example, a geometric distribution is simulated using a candidate transition law such that the states need not reading. The second and third examples exploit the fact that there are no added complications when simulating continuous or multivariate distributions, provided that the minimal point of the IMH chain can be identified.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60K30
zbMATH DE Number: 1790181
zbMATH Keywords: Metropolis algorithms
zbMATH Keywords: Hastings algorithms
zbMATH Keywords: Markov chains
zbMATH Keywords: perfect sampling algorithms
zbMATH Keywords: invariant measure
zbMATH Keywords: backwards coupling
zbMATH Keywords: coupling from the past
author: Jem N. Corcoran
author: R. L. Tweedie
MaRDI profile type: Publication
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full work available at URL: s0378-3758(01)00243-9
OpenAlex ID: W1981165469
description: scientific article; zbMATH DE number 1790181