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Looking at Markov samplers through cusum path plots: a simple diagnostic idea

Looking at Markov samplers through cusum path plots: a simple diagnostic idea In this paper, we propose to monitor a Markov chain sampler using the cusum path plot of a chosen one-dimensional summary statistic. We argue that the cusum path plot can bring out, more effectively than the sequential plot, those aspects of a Markov sampler which tell the user how quickly or slowly the sampler is moving around in its sample space, in the direction of the summary statistic. The proposal is then illustrated in four examples which represent situations where the cusum path plot works well and not well. Moreover, a rigorous analysis is given for one of the examples. We conclude that the cusum path plot is an effective tool for convergence diagnostics of a Markov sampler and for comparing different Markov samplers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistics and Computing Springer Journals

Looking at Markov samplers through cusum path plots: a simple diagnostic idea

Statistics and Computing , Volume 8 (3) – Oct 7, 2004

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References (24)

Publisher
Springer Journals
Copyright
Copyright © 1998 by Kluwer Academic Publishers
Subject
Statistics; Data Structures, Cryptology and Information Theory; Numeric Computing; Mathematical Modeling and Industrial Mathematics; Statistics, general
ISSN
0960-3174
eISSN
1573-1375
DOI
10.1023/A:1008917713940
Publisher site
See Article on Publisher Site

Abstract

In this paper, we propose to monitor a Markov chain sampler using the cusum path plot of a chosen one-dimensional summary statistic. We argue that the cusum path plot can bring out, more effectively than the sequential plot, those aspects of a Markov sampler which tell the user how quickly or slowly the sampler is moving around in its sample space, in the direction of the summary statistic. The proposal is then illustrated in four examples which represent situations where the cusum path plot works well and not well. Moreover, a rigorous analysis is given for one of the examples. We conclude that the cusum path plot is an effective tool for convergence diagnostics of a Markov sampler and for comparing different Markov samplers.

Journal

Statistics and ComputingSpringer Journals

Published: Oct 7, 2004

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