Exact simulation of Poisson-Dirichlet distribution and generalised gamma process

Dassios, Angelos ORCID: 0000-0002-3968-2366 and Zhang, Junyi ORCID: 0000-0001-8986-6588 (2023) Exact simulation of Poisson-Dirichlet distribution and generalised gamma process. Methodology and Computing in Applied Probability, 25 (2). ISSN 1387-5841

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Abstract

Let J1> J2> ⋯ be the ranked jumps of a gamma process τα on the time interval [0 , α] , such that τα=∑k=1∞Jk . In this paper, we design an algorithm that samples from the random vector (J1,⋯,JN,∑k=N+1∞Jk) . Our algorithm provides an analog to the well-established inverse Lévy measure (ILM) algorithm by replacing the numerical inversion of exponential integral with an acceptance-rejection step. This research is motivated by the construction of Dirichlet process prior in Bayesian nonparametric statistics. The prior assigns weight to each atom according to a GEM distribution, and the simulation algorithm enables us to sample from the N largest random weights of the prior. Then we extend the simulation algorithm to a generalised gamma process. The simulation problem of inhomogeneous processes will also be considered. Numerical implementations are provided to illustrate the effectiveness of our algorithms.

Item Type:	Article
Official URL:	https://www.springer.com/journal/11009
Additional Information:	© 2023 The Author(s).
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics
Date Deposited:	14 Jul 2023 14:18
Last Modified:	25 Apr 2024 18:15
URI:	http://eprints.lse.ac.uk/id/eprint/119755

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