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August 2011 Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modeling
James P. Hobert, Vivekananda Roy, Christian P. Robert
Statist. Sci. 26(3): 332-351 (August 2011). DOI: 10.1214/11-STS365

Abstract

The reversible Markov chains that drive the data augmentation (DA) and sandwich algorithms define self-adjoint operators whose spectra encode the convergence properties of the algorithms. When the target distribution has uncountable support, as is nearly always the case in practice, it is generally quite difficult to get a handle on these spectra. We show that, if the augmentation space is finite, then (under regularity conditions) the operators defined by the DA and sandwich chains are compact, and the spectra are finite subsets of [0, 1). Moreover, we prove that the spectrum of the sandwich operator dominates the spectrum of the DA operator in the sense that the ordered elements of the former are all less than or equal to the corresponding elements of the latter. As a concrete example, we study a widely used DA algorithm for the exploration of posterior densities associated with Bayesian mixture models [J. Roy. Statist. Soc. Ser. B 56 (1994) 363–375]. In particular, we compare this mixture DA algorithm with an alternative algorithm proposed by Frühwirth-Schnatter [J. Amer. Statist. Assoc. 96 (2001) 194–209] that is based on random label switching.

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James P. Hobert. Vivekananda Roy. Christian P. Robert. "Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modeling." Statist. Sci. 26 (3) 332 - 351, August 2011. https://doi.org/10.1214/11-STS365

Information

Published: August 2011
First available in Project Euclid: 31 October 2011

zbMATH: 1246.60095
MathSciNet: MR2918006
Digital Object Identifier: 10.1214/11-STS365

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.26 • No. 3 • August 2011
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