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How useful Bayesian inference could be in Model-based clustering?

Last modified: 2013-06-14

#### Abstract

Since about twenty years, Bayesian inference for finite mixture analysis received much attention and a lot of contributions (see for instance the book of Frühwirth-Schnatter 2006). Despite well-documented drawbacks (difficulty to use non informative priors, label switching identifiability problem), Bayesian inference for mixture could be useful in a density estimation context in a low or moderate dimension setting. But Full Bayesian inference is seldom employed in a Model-based clustering context where recovering the unknown labels is of first interest and where the user is often concerned with high dimensional data. In this communication, we analyse the pro and the con of Bayesian inference in the model-based clustering context. We exhibit situations where its main drawbacks can be avoided or circumvented. We will focus attention on the latent class model for categorical data. In particular, in this context, it is possible to derive (completed) integrated likelihoods without requiring asymptotic approximations. We highlight the interest and the traps of the resulting model selection criteria.

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