Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a nonparametric Bayesian approach to estimate the intensity of the underlying Poisson process and the distribution of the jumps. We provide a Markov chain Monte Carlo scheme for obtaining samples from the posterior. We apply our method on both simulated and real data examples, and compare its performance with the frequentist plug-in estimator proposed by Buchmann and Grübel. On a theoretical side, we study the posterior from the frequentist point of view and prove that as the sample size n→∞, it contracts around the “true,” data-generating parameters at rate 1/√n, up to a n factor.

Original languageEnglish
Pages (from-to)1-29
Number of pages29
JournalScandinavian Journal of Statistics
Publication statusPublished - 2019

    Research areas

  • compound Poisson process, data augmentation, diophantine equation, Gibbs sampler, Metropolis-Hastings algorithm, Nonparametric Bayesian estimation

ID: 67653400