Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modelling
Robert, Christian P.; Roy, Vivekananda; Hobert, James P. (2011), Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modelling, Statistical Science, 26, 3, p. 332-351. http://dx.doi.org/10.1214/11-STS365
TypeArticle accepté pour publication ou publié
Journal nameStatistical Science
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Abstract (EN)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 (Diebolt and Robert, 1994). In particular, we compare this mixture DA algorithm with an alternative algorithm proposed by Frühwirth-Schnatter (2001) that is based on random label switching.
Subjects / KeywordsMarkov chains; Data augmentation; sandwich algorithms; Bayesian mixture models
Showing items related by title and author.
Using a Markov Chain to Construct a Tractable Approximation of an Intractable Probability Distribution Hobert, James P.; Jones, Galin L.; Robert, Christian P. (2006) Article accepté pour publication ou publié