Posterior contraction rates for support boundary recovery

Abstract

Given a sample of a Poisson point process with intensity ${\lambda }_f(x,y)=n1(f(x)\le y),$ 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.