Mixture models, latent variables and partitioned importance sampling

Casella, George; Robert, Christian P.; Wells, Martin T.

Casella, George; Robert, Christian P.; Wells, Martin T. (2004), Mixture models, latent variables and partitioned importance sampling, Statistical Methodology, 1, 1-2, p. 1-18. http://dx.doi.org/10.1016/j.stamet.2004.05.001

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Type

Article accepté pour publication ou publié

Date

2004

Journal name

Statistical Methodology

Volume

Number

1-2

Publisher

Elsevier

Pages

1-18

Abstract (EN)

Gibbs sampling has had great success in the analysis of mixture models. In particular, the “latent variable” formulation of the mixture model greatly reduces computational complexity. However, one failing of this approach is the possible existence of almost-absorbing states, called trapping states, as it may require an enormous number of iterations to escape from these states. Here we examine an alternative approach to estimation in mixture models, one based on a Rao–Blackwellization argument applied to a latent-variable-based estimator. From this derivation we construct an alternative Monte Carlo sampling scheme that avoids trapping states.

Subjects / Keywords

Monte Carlo methods; Bayes estimation; Partition decomposition; Posterior probabilities; Gibbs sampling

JEL

C11 - Bayesian Analysis: General
C15 - Statistical Simulation Methods: General