Decompounding discrete distributions: A nonparametric Bayesian approach

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Abstract
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 , up to a factor.
Funding Information
  • Deutsche Forschungsgemeinschaft (CRC 1294 Data Assimilation, DFG 314838170, GRK 2297 MathCoRe)
  • H2020 European Research Council (ERC Grant Agreement 320637)

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