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.
Acknowledgments
We are grateful to the editor and two reviewers for giving us detailed and constructive comments. The comments have helped us a lot in improving the manuscript. We also wish to thank Prof. Igor Prünster for kindly reading the draft and giving us helpful suggestions.
Citation
Junyi Zhang. Angelos Dassios. "Posterior Sampling From Truncated Ferguson-Klass Representation of Normalised Completely Random Measure Mixtures." Bayesian Anal. Advance Publication 1 - 31, 2024. https://doi.org/10.1214/24-BA1421
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