Bayesian Modelling and Inference on Mixtures of Distributions

Marin, Jean‐Michel; Mengersen, Kerrie; Robert, Christian P.

doi:10.1016/s0169-7161(05)25016-2

Cited by 322 publications

(364 citation statements)

References 99 publications

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“…< µ K , or equally the same constraint on the mixture proportions, or the component variances. More sophisticated alternatives can be found, for example, in Marin et al [2005].…”

Section: Identifiability Constraintsmentioning

confidence: 99%

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

2009

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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.

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“…< µ K , or equally the same constraint on the mixture proportions, or the component variances. More sophisticated alternatives can be found, for example, in Marin et al [2005].…”

Section: Identifiability Constraintsmentioning

confidence: 99%

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

2009

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“…Mixture model called the particular model because this model is able to combine some different data but still retains the characteristics of the original data (McLachlan and Basford, 1988;Gelman et al, 1995;Astuti, 2006). This model will able to provide flexible parametric framework in modeling and statistical analysis (Marin et al, 2005).…”

Section: Mixture Modelsmentioning

confidence: 99%

An Algorithm for Determining the Number of Mixture Components on the Bayesian Mixture Model Averaging for Microarray Data

Astuti¹,

Iriawan²,

Irhamah³

et al. 2015

Journal of Mathematics and Statistics

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The major challenges on the statistical analysis of microarray data are the limited availability of samples, large number of measured variables and the complexity of distribution of the data obtained (e.g., multimodal). These phenomena could be considered in Bayesian method, used Bayesian Mixture Model (BMM) methods and Bayesian Model Averaging (BMA) methods. Modeling of Bayesian Mixture Model Averaging (BMMA) for microarray data was developed based on these two studies. One of the most important stages in BMMA is determination of the number of mixture components in the data setting as the most appropriate BMMA models. This paper proposes an algorithm for determining the number of mixture components in BMMA for microarray data. The algorithm is developed based on the simulation data generated from a case study of Indonesian and it has been implemented on the outside Indonesian microarray data. The results have succed to demonstrate two step algorithms, called Preliminary Process and Smoothing Process Algorithms, to the Indonesian case microarray data with the accuracy rate of 99.3690% and 99.9094% for the outside Indonesian microarray data.

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“…Mixture model [39] is a probabilistic model originally proposed to address the multi-modal problem in the data, and now is frequently used for the task of clustering in data mining, machine learning and statistics. Generally, a mixture model defines the distribution of a random variable, which contains multiple components and each component represents a different distribution following the same distribution family but with different parameters.…”

Section: Mixture Modelsmentioning

confidence: 99%

Probabilistic Models for Text Mining

Sun

Deng

2012

Mining Text Data

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A number of probabilistic methods such as LDA, hidden Markov models, Markov random fields have arisen in recent years for probabilistic analysis of text data. This chapter provides an overview of a variety of probabilistic models for text mining. The chapter focuses more on the fundamental probabilistic techniques, and also covers their various applications to different text mining problems. Some examples of such applications include topic modeling, language modeling, document classification, document clustering, and information extraction.

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Bayesian Modelling and Inference on Mixtures of Distributions

Cited by 322 publications

References 99 publications

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

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

An Algorithm for Determining the Number of Mixture Components on the Bayesian Mixture Model Averaging for Microarray Data

Probabilistic Models for Text Mining

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