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

Zhang, Junyi ORCID: 0000-0001-8986-6588 and Dassios, Angelos ORCID: 0000-0002-3968-2366 (2024) Posterior sampling from truncated Ferguson-Klass representation of normalised completely random measure mixtures. Bayesian Analysis. ISSN 1936-0975

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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.

Item Type:	Article
Additional Information:	© 2024 The Author(s)
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	06 Mar 2024 17:06
Last Modified:	17 Oct 2024 18:11
URI:	http://eprints.lse.ac.uk/id/eprint/122228

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