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.
Publié le : 1998-02-14
Classification:
Markov chain Monte Carlo,
Peskun's
theorem,
mixture kernels,
60J05,
65C05,
62-04
@article{1027961031,
author = {Tierney, Luke},
title = {A note on Metropolis-Hastings kernels for general state
spaces},
journal = {Ann. Appl. Probab.},
volume = {8},
number = {1},
year = {1998},
pages = { 1-9},
language = {en},
url = {http://dml.mathdoc.fr/item/1027961031}
}
Tierney, Luke. A note on Metropolis-Hastings kernels for general state
spaces. Ann. Appl. Probab., Tome 8 (1998) no. 1, pp. 1-9. http://gdmltest.u-ga.fr/item/1027961031/