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February 1998 MCMC convergence diagnosis via multivariate bounds on log-concave densities
Stephen P. Brooks
Ann. Statist. 26(1): 398-433 (February 1998). DOI: 10.1214/aos/1030563991

Abstract

We begin by showing how piecewise linear bounds may be devised, which bound both above and below any concave log-density in general dimensions. We then show how these bounds may be used to gain an upper bound to the volume in the tails outside the convex hull of the sample path in order to assess how well the sampler has explored the target distribution. This method can be used as a stand-alone diagnostic to determine when the sampler output provides a reliable basis for inference on the stationary density, or in conjunction with existing convergence diagnostics to ensure that they are based upon good sampler output. We provide an example and briefly discuss possible extensions to the method and alternative applications of the bounds.

Citation

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Stephen P. Brooks. "MCMC convergence diagnosis via multivariate bounds on log-concave densities." Ann. Statist. 26 (1) 398 - 433, February 1998. https://doi.org/10.1214/aos/1030563991

Information

Published: February 1998
First available in Project Euclid: 28 August 2002

zbMATH: 0961.65002
MathSciNet: MR1608152
Digital Object Identifier: 10.1214/aos/1030563991

Subjects:
Primary: 00A72 , 65C05
Secondary: 62F15 , 65C10

Keywords: bounds , estimation , Markov chain Monte Carlo , simulation , tail probability

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 1 • February 1998
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