Exact simulation of Poisson-Dirichlet distribution and generalised gamma process

Angelos Dassios and Junyi Zhang

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: exact simulation; gamma process; generalised gamma process; Lévy process; Poisson-Dirichlet distribution (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2023-06-10
New Economics Papers: this item is included in nep-ecm
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Published in Methodology and Computing in Applied Probability, 10, June, 2023, 25(2). ISSN: 1387-5841

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