Posterior contraction rates for support boundary recovery

Markus Reiss, Anselm Johannes Schmidt-Hieber*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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 languageEnglish
Pages (from-to)6638
Number of pages6656
JournalStochastic processes and their applications
Volume130
Issue number11
DOIs
Publication statusPublished - 1 Nov 2020

Keywords

  • UT-Hybrid-D
  • Posterior contraction
  • Poisson point process
  • Boundary detection
  • Gaussian prior
  • Wavelet prior
  • Frequentist Bayesian analysis

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