{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/decompounding-discrete-distributions-a-non","title":"Decompounding discrete distributions: A non-parametric Bayesian approach","arxiv_id":"1903.11142","date":"2019-03-26","proceeding":null,"authors":["Shota Gugushvili","Ester Mariucci","Frank van der Meulen"],"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 non-parametric Bayesian approach to estimate the intensity of the underlying Poisson process and the distribution of the jumps. We provide a MCMC 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 Gr\\\"ubel. On a theoretical side, we study the posterior from the frequentist point of view and prove that as the sample size $n\\rightarrow\\infty$, it contracts around the `true', data-generating parameters at rate $1/\\sqrt{n}$, up to a $\\log n$ factor.","url_abs":"http://arxiv.org/abs/1903.11142v2","url_pdf":"http://arxiv.org/pdf/1903.11142v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"decompounding-discrete-distributions-a-non","repo_url":"https://github.com/fmeulen/Bdd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}