Exact Simulation of Poisson-Dirichlet Distribution and Generalised Gamma Process

Angelos Dassios, Junyi Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

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.

Original languageEnglish
Article number64
Pages (from-to)1-21
Number of pages21
JournalMethodology and Computing in Applied Probability
Volume25
Issue number2
DOIs
Publication statusPublished - Jun 2023

Keywords

  • 60J25
  • 62F15
  • 62G05
  • Exact simulation
  • Gamma process
  • Generalised gamma process
  • Lévy process
  • Poisson-Dirichlet distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics

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