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Exact simulation of Poisson-Dirichlet distribution and generalised gamma process

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  • Dassios, Angelos
  • Zhang, Junyi

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.

Suggested Citation

  • Dassios, Angelos & Zhang, Junyi, 2023. "Exact simulation of Poisson-Dirichlet distribution and generalised gamma process," LSE Research Online Documents on Economics 119755, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:119755
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    File URL: http://eprints.lse.ac.uk/119755/
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    More about this item

    Keywords

    exact simulation; gamma process; generalised gamma process; Lévy process; Poisson-Dirichlet distribution;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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