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Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery. (English) Zbl 1452.62155
The paper presents the performance of compound Poisson (CPP) as nonparametric priors. It is proved that under (CPP) priors, optimal posterior contraction rates are attained for Hölder functions and for monotone functions. In Section 2, the contraction rates for compound Poisson processes and subordinator priors are investigated. A general description of the asymptotic posterior shape in which the results thereafter can be embedded is presented in Section 3. In Section 4, Bernstein-von Mises-type theorems and results on the frequentist coverage of credible sets for CPP priors are presented. The proofs of the new theorems are presented in two appendices.

62C10 Bayesian problems; characterization of Bayes procedures
62G05 Nonparametric estimation
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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