Smooth Estimates of Normal Mixtures

Barbara Tong and Kert Viele

Abstract:

Posterior distributions for mixture models often have multiple modes, particularly near the boundaries of the parameter space where the component variances are small. This multimodality results in predictive densities that are extremely rough. We propose an adjustment of the standard Normal-Inverse Gamma prior structure that directly controls the ratio of the largest component variance to the smallest component variance. The prior adjustment smooths out modes near the boundary of the parameter space, producing more reasonable estimates of the predictive density.

Keywords: Predictive Density, Markov Chain Monte Carlo

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