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