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Posterior contraction rates for support boundary recovery

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  • Reiß, Markus
  • Schmidt-Hieber, Johannes

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.

Suggested Citation

  • Reiß, Markus & Schmidt-Hieber, Johannes, 2020. "Posterior contraction rates for support boundary recovery," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6638-6656.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:11:p:6638-6656
    DOI: 10.1016/j.spa.2020.06.005
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    References listed on IDEAS

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    1. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265, December.
    2. Victor Chernozhukov & Han Hong, 2004. "Likelihood Estimation and Inference in a Class of Nonregular Econometric Models," Econometrica, Econometric Society, vol. 72(5), pages 1445-1480, September.
    3. Wang, Yazhen, 1997. "Small ball problem via wavelets for Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 133-139, March.
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    Cited by:

    1. Onizuka, Takahiro & Iwashige, Fumiya & Hashimoto, Shintaro, 2024. "Bayesian boundary trend filtering," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).

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