Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modelling

James Hobert, Christian Robert and Vivekanada Roy
Additional contact information
James Hobert: Crest
Christian Robert: Crest
Vivekanada Roy: Crest

No 2010-29, Working Papers from Center for Research in Economics and Statistics

Abstract: Every reversible Markov chain defines an operator whose spectrum encodes the convergenceproperties of the chain. When the state space is finite, the spectrum is just the set ofeigenvalues of the corresponding Markov transition matrix. However, when the state space isinfinite, the spectrum may be uncountable, and is nearly always impossible to calculate. In mostapplications of the data augmentation (DA) algorithm, the state space of the DA Markov chainis infinite. However, we show that, under regularity conditions that include the finiteness of theaugmented space, the operators defined by the DA chain and Hobert and Marchev’s (2008) alternativechain are both compact, and the corresponding spectra are both finite subsets of [0; 1).Moreover, we prove that the spectrum of Hobert and Marchev’s (2008) chain dominates thespectrum of the DA chain in the sense that the ordered elements of the former are all less thanor equal to the corresponding elements of the latter. As a concrete example, we study a widelyused DA algorithm for the exploration of posterior densities associated with Bayesian mixturemodels (Diebolt and Robert, 1994). In particular, we compare this mixture DA algorithm withan alternative algorithm proposed by Fr¨uhwirth-Schnatter (2001) that is based on random labelswitching.

Pages: 38
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://crest.science/RePEc/wpstorage/2010-29.pdf Crest working paper version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:crs:wpaper:2010-29

Access Statistics for this paper

More papers in Working Papers from Center for Research in Economics and Statistics Contact information at EDIRC.
Bibliographic data for series maintained by Secretariat General () and Murielle Jules Maintainer-Email : murielle.jules@ensae.Fr.