Hypothesis Tests of Convergence in Markov Chain Monte
Carlo
Angelo J. Canty
Abstract
Deciding when a Markov chain has reached its stationary distribution is a
major problem in applications of Markov Chain Monte Carlo methods.
Many methods have been proposed ranging from simple
graphical methods to complicated numerical methods. Most such methods
require a lot of user interaction with the chain which can be very tedious and
time-consuming for a slowly mixing chain.
This article describes a system to reduce the burden on
the user in assessing convergence. The method uses simple
nonparametric hypothesis testing techniques to examine the output of
several independent chains and so determines whether there is any evidence against
the hypothesis of convergence. We illustrate the proposed
method on some examples from the literature.
Keywords: Convergence diagnostic; Gibbs sampler; Nonparametric test;
Permutation test.
This article was published in the Journal of Computational and Graphical
Statistics(1999), 8, 93-108.
This page is maintained by Angelo Canty,
cantya@mcmaster.ca
Last updated on July 23, 2001