Posterior contraction rates for support boundary recovery

Markus Reiss; Johannes Schmidt-Hieber

doi:10.1016/j.spa.2020.06.005

Posterior contraction rates for support boundary recovery

Markus Reiss
, Johannes Schmidt-Hieber^*

^*Corresponding author for this work

Mathematics of Operations Research

Research output: Contribution to journal › Article › Academic › peer-review

2 Citations (Scopus)

417 Downloads (Pure)

Abstract

Given a sample of a Poisson point process with intensity
λf(x,y)=n1(f(x)≤y), we study recovery of the boundary function f from a nonparametric Bayes perspective. Because of the irregularity of this model, the analysis is non-standard. We establish a general result for the posterior contraction rate with respect to the L1-norm based on entropy and one-sided small probability bounds. From this, specific posterior contraction results are derived for Gaussian process priors and priors based on random wavelet series.

Original language	English
Pages (from-to)	6638
Number of pages	6656
Journal	Stochastic processes and their applications
Volume	130
Issue number	11
DOIs	https://doi.org/10.1016/j.spa.2020.06.005
Publication status	Published - 1 Nov 2020

Keywords

UT-Hybrid-D
Posterior contraction
Poisson point process
Boundary detection
Gaussian prior
Wavelet prior
Frequentist Bayesian analysis
22/2 OA procedure

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N2 - Given a sample of a Poisson point process with intensity λf(x,y)=n1(f(x)≤y), we study recovery of the boundary function f from a nonparametric Bayes perspective. Because of the irregularity of this model, the analysis is non-standard. We establish a general result for the posterior contraction rate with respect to the L1-norm based on entropy and one-sided small probability bounds. From this, specific posterior contraction results are derived for Gaussian process priors and priors based on random wavelet series.

AB - Given a sample of a Poisson point process with intensity λf(x,y)=n1(f(x)≤y), we study recovery of the boundary function f from a nonparametric Bayes perspective. Because of the irregularity of this model, the analysis is non-standard. We establish a general result for the posterior contraction rate with respect to the L1-norm based on entropy and one-sided small probability bounds. From this, specific posterior contraction results are derived for Gaussian process priors and priors based on random wavelet series.

KW - UT-Hybrid-D

KW - Posterior contraction

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KW - Boundary detection

KW - Gaussian prior

KW - Wavelet prior

KW - Frequentist Bayesian analysis

KW - 22/2 OA procedure

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JF - Stochastic processes and their applications

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ER -

Posterior contraction rates for support boundary recovery

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Keywords

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