Brazilian Journal of Probability and Statistics

Keeping the balance—Bridge sampling for marginal likelihood estimation in finite mixture, mixture of experts and Markov mixture models

Sylvia Frühwirth-Schnatter

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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.

Article information

Braz. J. Probab. Stat., Volume 33, Number 4 (2019), 706-733.

Received: February 2019
Accepted: April 2019
First available in Project Euclid: 26 August 2019

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Mathematical Reviews number (MathSciNet)

Markov chain Monte Carlo model-based clustering Gaussian mixtures hierarchical priors permutation sampling importance sampling


Frühwirth-Schnatter, Sylvia. Keeping the balance—Bridge sampling for marginal likelihood estimation in finite mixture, mixture of experts and Markov mixture models. Braz. J. Probab. Stat. 33 (2019), no. 4, 706--733. doi:10.1214/19-BJPS446.

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