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

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  • Zhang, Junyi
  • Dassios, Angelos

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.

Suggested Citation

  • Zhang, Junyi & Dassios, Angelos, 2025. "Posterior sampling from truncated Ferguson-Klass representation of normalised completely random measure mixtures," LSE Research Online Documents on Economics 122228, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:122228
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    References listed on IDEAS

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    1. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
    2. François Caron & Emily B. Fox, 2017. "Sparse graphs using exchangeable random measures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1295-1366, November.
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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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