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November 2019 Keeping the balance—Bridge sampling for marginal likelihood estimation in finite mixture, mixture of experts and Markov mixture models
Sylvia Frühwirth-Schnatter
Braz. J. Probab. Stat. 33(4): 706-733 (November 2019). DOI: 10.1214/19-BJPS446

Abstract

Finite mixture models and their extensions to Markov mixture and mixture of experts models are very popular in analysing data of various kind. A challenge for these models is choosing the number of components based on marginal likelihoods. The present paper suggests two innovative, generic bridge sampling estimators of the marginal likelihood that are based on constructing balanced importance densities from the conditional densities arising during Gibbs sampling. The full permutation bridge sampling estimator is derived from considering all possible permutations of the mixture labels for a subset of these densities. For the double random permutation bridge sampling estimator, two levels of random permutations are applied, first to permute the labels of the MCMC draws and second to randomly permute the labels of the conditional densities arising during Gibbs sampling. Various applications show very good performance of these estimators in comparison to importance and to reciprocal importance sampling estimators derived from the same importance densities.

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Sylvia Frühwirth-Schnatter. "Keeping the balance—Bridge sampling for marginal likelihood estimation in finite mixture, mixture of experts and Markov mixture models." Braz. J. Probab. Stat. 33 (4) 706 - 733, November 2019. https://doi.org/10.1214/19-BJPS446

Information

Received: 1 February 2019; Accepted: 1 April 2019; Published: November 2019
First available in Project Euclid: 26 August 2019

zbMATH: 07120730
MathSciNet: MR3996313
Digital Object Identifier: 10.1214/19-BJPS446

Rights: Copyright © 2019 Brazilian Statistical Association

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Vol.33 • No. 4 • November 2019
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