Posterior contraction rates for support boundary recovery

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...

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Bibliographic Details
Published in:Stochastic processes and their applications 2020-11, Vol.130 (11), p.6638-6656
Main Authors: Reiß, Markus, Schmidt-Hieber, Johannes
Format: Article
Language:English
Subjects:
Boundary detection
Frequentist Bayesian analysis
Gaussian prior
Poisson point process
Posterior contraction
Wavelet prior
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2020.06.005