Bayesian analysis of mixture modelling using the multivariate t distribution

Authors:
Tsung I. Lin;Jack C. Lee;Huey F. Ni
Affiliations:
Department of Statistics, Tunghai University, Taiwan. tilin@mail.thu.edu.tw;Institute of Statistics and Graduate Institute of Finance, National Chiao Tung University, Taiwan;Institute of Statistics, National Chiao Tung University, Taiwan
Venue:
Statistics and Computing
Year:
2004

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Abstract

A finite mixture model using the multivariate t distribution has been shown as a robust extension of normal mixtures. In this paper, we present a Bayesian approach for inference about parameters of t-mixture models. The specifications of prior distributions are weakly informative to avoid causing nonintegrable posterior distributions. We present two efficient EM-type algorithms for computing the joint posterior mode with the observed data and an incomplete future vector as the sample. Markov chain Monte Carlo sampling schemes are also developed to obtain the target posterior distribution of parameters. The advantages of Bayesian approach over the maximum likelihood method are demonstrated via a set of real data.