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

Zhang Junyi, Hong Kong Polytechnic University
Dassios Angelos, London School of Economics

In this talk, we discuss 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 present 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 network model. Examples and numerical implementations will be given based on the gamma, stable and generalised gamma processes.

Area: CS59 - Dependent random measures: evolution and inference (Dario Spanò)

Keywords: Bayesian nonparametric statistics, completely random measures, blocked Gibbs sampler, generalised gamma process

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