Mixture models are widely used, in a vaste range of applied fields, to model heterogeneity in the data, or as flexible modeling tools. In this paper we focus on the role of mixtures in Bayesian nonparametrics. Based on results by Feller, we present a constructive approximation scheme of (random) distribution functions by mixtures. We obtain a general framework to study nonparametric priors based on mixtures. We review some recent results for the univariate case, in particular on consistency of the posterior distribution. Then, we present novel extensions to the multivariate case.
On the role of mixtures in Bayesian nonparametrics
PETRONE, SONIA
2004
Abstract
Mixture models are widely used, in a vaste range of applied fields, to model heterogeneity in the data, or as flexible modeling tools. In this paper we focus on the role of mixtures in Bayesian nonparametrics. Based on results by Feller, we present a constructive approximation scheme of (random) distribution functions by mixtures. We obtain a general framework to study nonparametric priors based on mixtures. We review some recent results for the univariate case, in particular on consistency of the posterior distribution. Then, we present novel extensions to the multivariate case.
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