The Annals of Applied Probability

A note on Metropolis-Hastings kernels for general state spaces

Luke Tierney

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab. Volume 8, Number 1 (1998), 1-9.

Dates
First available in Project Euclid: 29 July 2002

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1027961031

Mathematical Reviews number (MathSciNet)
MR1620401

Digital Object Identifier
doi:10.1214/aoap/1027961031

Zentralblatt MATH identifier
0935.60053

Subjects
Primary: 60J05: Discrete-time Markov processes on general state spaces 65C05: Monte Carlo methods 62-04: Explicit machine computation and programs (not the theory of computation or programming)

Keywords
Markov chain Monte Carlo Peskun's theorem mixture kernels

Citation

Tierney, Luke. A note on Metropolis-Hastings kernels for general state spaces. Ann. Appl. Probab. 8 (1998), no. 1, 1--9. doi:10.1214/aoap/1027961031. http://projecteuclid.org/euclid.aoap/1027961031.


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