PRACTICAL BAYESIAN DENSITY-ESTIMATION USING MIXTURES OF NORMALS

Mixtures of normals provide a flexible model for estimating densities in a Bayesian framework. There are some difficulties with this model, however. First, standard reference priors yield improper posteriors. S econd, the posterior for the number of components in the mixture is no t well defined (if the reference prior is used). Third, posterior simu lation does not provide a direct estimate of the posterior for the num ber of components. We present some practical methods for coping with t hese 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.