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June 2020 Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery
Markus Reiß, Johannes Schmidt-Hieber
Ann. Statist. 48(3): 1432-1451 (June 2020). DOI: 10.1214/19-AOS1853

Abstract

Given data from a Poisson point process with intensity $(x,y)\mapston\mathbf{1}(f(x)\leq y)$, frequentist properties for the Bayesian reconstruction of the support boundary function $f$ are derived. We mainly study compound Poisson process priors with fixed intensity proving that the posterior contracts with nearly optimal rate for monotone support boundaries and adapts to Hölder smooth boundaries. We then derive a limiting shape result for a compound Poisson process prior and a function space with increasing parameter dimension. It is shown that the marginal posterior of the mean functional performs an automatic bias correction and contracts with a faster rate than the MLE. In this case, $(1-\alpha )$-credible sets are also asymptotic $(1-\alpha )$-confidence intervals. As a negative result, it is shown that the frequentist coverage of credible sets is lost for linear functions $f$ outside the function class.

Citation

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Markus Reiß. Johannes Schmidt-Hieber. "Nonparametric Bayesian analysis of the compound Poisson prior for support boundary recovery." Ann. Statist. 48 (3) 1432 - 1451, June 2020. https://doi.org/10.1214/19-AOS1853

Information

Received: 1 September 2018; Revised: 1 February 2019; Published: June 2020
First available in Project Euclid: 17 July 2020

zbMATH: 07241597
MathSciNet: MR4124329
Digital Object Identifier: 10.1214/19-AOS1853

Subjects:
Primary: 62C10, 62G05
Secondary: 60G55

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 3 • June 2020
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