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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Text (Exact Simulation of Poisson-Dirichlet Distribution and Generalised Gamma Process)
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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: | 12 Dec 2024 03:48 |
| URI: | http://eprints.lse.ac.uk/id/eprint/119755 |
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