Mixture models are a useful tool for analysing complex data. The Bayesian approach to inference offers a vast choice of prior laws on the mixing measure, which induce priors on the mixture density. The posterior distribution of any summary of the mixing distribution can be derived. This note reviews the current status of mixture density estimation, focussing on recent results on posterior contraction rates for the mixing distribution in the 1-Wasserstein metric. Viewing the mixing measure as a genuine prior, the single mixing parameters can be estimated exploiting the relationship, formalized by Tweedie’s formula, with the marginal density.
Empirical Bayes estimation for mixture models
Catia Scricciolo
2020-01-01
Abstract
Mixture models are a useful tool for analysing complex data. The Bayesian approach to inference offers a vast choice of prior laws on the mixing measure, which induce priors on the mixture density. The posterior distribution of any summary of the mixing distribution can be derived. This note reviews the current status of mixture density estimation, focussing on recent results on posterior contraction rates for the mixing distribution in the 1-Wasserstein metric. Viewing the mixing measure as a genuine prior, the single mixing parameters can be estimated exploiting the relationship, formalized by Tweedie’s formula, with the marginal density.
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