Compound random measures and their use in Bayesian nonparametrics

2014/10/02 by Jim E. Griffin, Fabrizio Leisen, Griffin, Jim E. +1 · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1410.0611

openalex publication_date 2014/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new class of dependent random measures which we call \it compound random measures are proposed and the use of normalized versions of these random measures as priors in Bayesian nonparametric mixture models is considered. Their tractability allows the properties of both compound random measures and normalized compound random measures to be derived. In particular, we show how compound random measures can be constructed with gamma, σ-stable and generalized gamma process marginals. We also derive several forms of the Laplace exponent and characterize dependence through both the Lévy copula and correlation function. A slice sampler and an augmented Pólya urn scheme sampler are described for posterior inference when a normalized compound random measure is used as the mixing measure in a nonparametric mixture model and a data example is discussed.

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