A priori truncation method for posterior sampling from homogeneous normalized completely random measure mixture models

Abstract

This paper adopts a Bayesian nonparametric mixture model where the mixing distribution belongs to the wide class of normalized homogeneous completely random measures. We propose a truncation method for the mixing distribution by discarding the weights of the unnormalized measure smaller than a threshold. We prove convergence in law of our approximation, provide some theoretical properties and characterize its posterior distribution so that a blocked Gibbs sampler is devised. The versatility of the approximation is illustrated by two different applications. In the first the normalized Bessel random measure, encompassing the Dirichlet process, is introduced; goodness of fit indexes show its good performances as mixing measure for density estimation. The second describes how to incorporate covariates in the support of the normalized measure, leading to a linear dependent model for regression and clustering.

arXiv comment32 pages, 6 figures, 2 tables

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• MCMC for Normalized Random Measure Mixture Models
• A marginal sampler for $\sigma$-Stable Poisson-Kingman mixture models
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