Approximate predetermined convergence properties of the Gibbs sampler
Approximate predetermined convergence properties of the Gibbs sampler
This article aims to provide a method for approximately predetermining convergence properties of the Gibbs sampler. This is to be done by first finding an approximate rate of convergence for a normal approximation of the target distribution. The rates of convergence for different implementation strategies of the Gibbs sampler are compared to find the best one. In general, the limiting convergence properties of the Gibbs sampler on a sequence of target distributions (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.
em algorithm, gaussian distribution, generalized linear models, hierarchical centering, laplace approximation, markhov chain
216-229
Roberts, G.O.
c954867f-84a1-4fc7-a618-ccbce35fa89b
Sahu, S.K.
33f1386d-6d73-4b60-a796-d626721f72bf
2001
Roberts, G.O.
c954867f-84a1-4fc7-a618-ccbce35fa89b
Sahu, S.K.
33f1386d-6d73-4b60-a796-d626721f72bf
Roberts, G.O. and Sahu, S.K.
(2001)
Approximate predetermined convergence properties of the Gibbs sampler.
Journal of Computational and Graphical Statistics, 10 (2), .
Abstract
This article aims to provide a method for approximately predetermining convergence properties of the Gibbs sampler. This is to be done by first finding an approximate rate of convergence for a normal approximation of the target distribution. The rates of convergence for different implementation strategies of the Gibbs sampler are compared to find the best one. In general, the limiting convergence properties of the Gibbs sampler on a sequence of target distributions (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.
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Published date: 2001
Keywords:
em algorithm, gaussian distribution, generalized linear models, hierarchical centering, laplace approximation, markhov chain
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Statistics
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Local EPrints ID: 30040
URI: http://eprints.soton.ac.uk/id/eprint/30040
ISSN: 1061-8600
PURE UUID: 08a19aa2-19c5-4875-93ee-4f030506c62c
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Date deposited: 11 May 2006
Last modified: 09 Jan 2022 03:03
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Author:
G.O. Roberts
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