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Compound Random Measures and their use in Bayesian nonparametrics

Griffin, Jim E., Leisen, Fabrizio (2017) Compound Random Measures and their use in Bayesian nonparametrics. Journal of the Royal Statistical Society Series B-Statistical Methodology, 79 (2). pp. 525-545. ISSN 1369-7412. E-ISSN 1467-9868. (doi:10.1111/rssb.12176) (KAR id:53655)

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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, ?-stable and generalized gamma process marginals. We also derive several forms of the Laplace exponent and characterize dependence through both the L\'evy copula and correlation function. A slice sampler and an augmented P\'olya 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.

Item Type: Article
DOI/Identification number: 10.1111/rssb.12176
Uncontrolled keywords: Dependent random measures; L\'evy Copula; Slice sampler; Mixture models; Multivariate L\'evy measures; Partial exchangeability
Subjects: H Social Sciences > HA Statistics
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Fabrizio Leisen
Date Deposited: 08 Jan 2016 22:24 UTC
Last Modified: 22 Mar 2021 16:45 UTC
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