Gareth O. Roberts,
Department of Mathematics and Statistics,
Lancaster University, Lancaster, LA1 4YF, UK.
Sujit K. Sahu,
Faculty of Mathematical Studies, University of Southampton, Highfield,
SO17 1BJ, UK.
June 15, 1999
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SUMMARY

The Gibbs sampler has proved to be a popular Markovian iterative scheme
for sampling from multi-dimensional distributions, especially for
applications within Bayesian statistics. Despite the existence of its more
general counterpart, the Metropolis-Hastings algorithm, the Gibbs sampler has
remained the default option for a wide range of problems.
However, the currently available analyses and the convergence assessment
methods of the Gibbs sampler are neither foolproof nor very powerful.

This article aims to provide a method for approximately
pre-determining convergence properties of the Gibbs sampler. This is to
be done by analysing the convergence properties of the Gibbs sampler
on a normal approximation of the target distribution. In
general, the limiting convergence properties of the Gibbs samplers on a
sequence of target distribution (approaching a limit) are not the same
as the convergence properties of the Gibbs sampler on the limiting
target distribution. Theoretical results are given in this article to
justify that under conditions, the convergence properties of the Gibbs
sampler can be approximated as well. A number of practical examples are
given for illustration.

You can get the paper in
plain postscript
or in
compressed postscript.

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S.K.Sahu@maths.soton.ac.uk