A Note on Metropolis-Hastings Kernels for General State Spaces
by Luke Tierney
Technical Report No. 606
School of Statistics
University of Minnesota
June 23, 1995
Research supported in part by grant DMS-9303557 from the National Science
Foundation.
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 using mixtures in Metropolis-Hastings kernels.