PRACTICAL BAYESIAN DENSITY ESTIMATION USING MIXTURES OF NORMALS

Kathryn Roeder and Larry Wasserman

Abstract:

Mixtures of normals provide a flexible model for estimating densities in a Bayesian framework. But there are some difficulties with this model. First, standard reference priors yield improper posteriors; second, the posterior for the number of components in the mixture is not well defined (if the reference prior is used) and third, posterior simulation does not provide a direct estimate of the posterior for the number of components. We present some practical methods for coping with these problems. Finally we give some results on the consistency of the method when the maximum number of components is allowed to grow with the sample size.

Keywords: Markov chain Monte Carlo, Normal mixture, Partially proper prior, Sieve.

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