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arXiv · 1703.08358

Posterior contraction rates for support boundary recovery

Markus Reiss·Johannes Schmidt-Hieber
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Abstract

Given a sample of a Poisson point process with intensity $\lambda_f(x,y) = n \mathbf{1}(f(x) \leq y),$ 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 $L^1$-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.

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Markus Reiss, Johannes Schmidt-Hieber. 2017-03-24. Posterior contraction rates for support boundary recovery. https://arxiv.org/abs/1703.08358

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