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February 1998 A note on Metropolis-Hastings kernels for general state spaces
Luke Tierney
Ann. Appl. Probab. 8(1): 1-9 (February 1998). DOI: 10.1214/aoap/1027961031


The Metropolis-Hastings algorithm is a method of constructing a reversible Markov transition kernel with a specified invariant distribution. This note describes necessary and sufficient conditions on the candidate generation kernel and the acceptance probability function for the resulting transition kernel and invariant distribution to satisfy the detailed balance conditions. A simple general formulation is used that covers a range of special cases treated separately in the literature. In addition, results on a useful partial ordering of finite state space reversible transition kernels are extended to general state spaces and used to compare the performance of two approaches to using mixtures in Metropolis-Hastings kernels.


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Luke Tierney. "A note on Metropolis-Hastings kernels for general state spaces." Ann. Appl. Probab. 8 (1) 1 - 9, February 1998.


Published: February 1998
First available in Project Euclid: 29 July 2002

zbMATH: 0935.60053
MathSciNet: MR1620401
Digital Object Identifier: 10.1214/aoap/1027961031

Primary: 60J05 , 62-04 , 65C05

Keywords: Markov chain Monte Carlo , mixture kernels , Peskun's theorem

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.8 • No. 1 • February 1998
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