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Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models.

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Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models. / Sperrin, Matthew; Jaki, Thomas; Wit, Ernst.

In: Statistics and Computing, Vol. 20, No. 3, 07.2010, p. 357-366.

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Sperrin, Matthew ; Jaki, Thomas ; Wit, Ernst. / Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models. In: Statistics and Computing. 2010 ; Vol. 20, No. 3. pp. 357-366.

Bibtex

@article{e1d1b551a0e847728f3d27dac04803b6,
title = "Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models.",
abstract = "The label switching problem is caused by the likelihood of a Bayesian mixture model being invariant to permutations of the labels. The permutation can change multiple times between Markov Chain Monte Carlo (MCMC) iterations making it difficult to infer component-specific parameters of the model. Various so-called {\textquoteleft}relabelling{\textquoteright} strategies exist with the goal to {\textquoteleft}undo{\textquoteright} the label switches that have occurred to enable estimation of functions that depend on component-specific parameters. Most existing approaches rely upon specifying a loss function, and relabelling by minimising its posterior expected loss. In this paper we develop probabilistic approaches to relabelling that allow estimation and incorporation of the uncertainty in the relabelling process. Variants of the probabilistic relabelling algorithm are introduced and compared to existing loss function based methods. We demonstrate that the idea of probabilistic relabelling can be expressed in a rigorous framework based on the EM algorithm.",
keywords = "Bayesian - Identifiability - Label switching - MCMC - Mixture model",
author = "Matthew Sperrin and Thomas Jaki and Ernst Wit",
year = "2010",
month = jul,
doi = "10.1007/s11222-009-9129-8",
language = "English",
volume = "20",
pages = "357--366",
journal = "Statistics and Computing",
issn = "0960-3174",
publisher = "Springer Netherlands",
number = "3",

}

RIS

TY - JOUR

T1 - Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models.

AU - Sperrin, Matthew

AU - Jaki, Thomas

AU - Wit, Ernst

PY - 2010/7

Y1 - 2010/7

N2 - The label switching problem is caused by the likelihood of a Bayesian mixture model being invariant to permutations of the labels. The permutation can change multiple times between Markov Chain Monte Carlo (MCMC) iterations making it difficult to infer component-specific parameters of the model. Various so-called ‘relabelling’ strategies exist with the goal to ‘undo’ the label switches that have occurred to enable estimation of functions that depend on component-specific parameters. Most existing approaches rely upon specifying a loss function, and relabelling by minimising its posterior expected loss. In this paper we develop probabilistic approaches to relabelling that allow estimation and incorporation of the uncertainty in the relabelling process. Variants of the probabilistic relabelling algorithm are introduced and compared to existing loss function based methods. We demonstrate that the idea of probabilistic relabelling can be expressed in a rigorous framework based on the EM algorithm.

AB - The label switching problem is caused by the likelihood of a Bayesian mixture model being invariant to permutations of the labels. The permutation can change multiple times between Markov Chain Monte Carlo (MCMC) iterations making it difficult to infer component-specific parameters of the model. Various so-called ‘relabelling’ strategies exist with the goal to ‘undo’ the label switches that have occurred to enable estimation of functions that depend on component-specific parameters. Most existing approaches rely upon specifying a loss function, and relabelling by minimising its posterior expected loss. In this paper we develop probabilistic approaches to relabelling that allow estimation and incorporation of the uncertainty in the relabelling process. Variants of the probabilistic relabelling algorithm are introduced and compared to existing loss function based methods. We demonstrate that the idea of probabilistic relabelling can be expressed in a rigorous framework based on the EM algorithm.

KW - Bayesian - Identifiability - Label switching - MCMC - Mixture model

U2 - 10.1007/s11222-009-9129-8

DO - 10.1007/s11222-009-9129-8

M3 - Journal article

VL - 20

SP - 357

EP - 366

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 3

ER -