Posterior sampling from truncated Ferguson-Klass representation of normalised completely random measure mixtures

Junyi Zhang and Angelos Dassios

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: In this paper, we study the finite approximation of the completely random measure (CRM) by truncating its Ferguson-Klass representation. The approximation is obtained by keeping the N largest atom weights of the CRM unchanged and combining the smaller atom weights into a single term.We develop the simulation algorithms for the approximation and characterise its posterior distribution, for which a blocked Gibbs sampler is devised.We demonstrate the usage of the approximation in two models. The first assumes such an approximation as the mixing distribution of a Bayesian nonparametric mixture model and leads to a finite approximation to the model posterior. The second concerns the finite approximation to the Caron-Fox model. Examples and numerical implementations are given based on the gamma, stable and generalised gamma processes.

Keywords: Bayesian nonparametric statistics; completely random measures; blocked Gibbs sampler; approximate inference; generalised gamma process (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2024-03-19
New Economics Papers: this item is included in nep-ecm
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Published in Bayesian Analysis, 19, March, 2024. ISSN: 1936-0975

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