Title: Nonparametric Bayesian analysis for support boundary recovery
Authors: Johannes Schmidt-Hieber - Leiden University (Netherlands) [presenting]
Markus Reiss - Humboldt University (Germany)
Abstract: Frequentist properties of the posterior distribution for a boundary detection problem are investigated. More specifically, given a sample of a Poisson point process with positive intensity above a boundary function $f$ and zero intensity below the boundary function, we study recovery of $f$ from a nonparametric Bayes perspective. Because of the irregularity of this model, the analysis is non-standard. We derive contraction rates for several classes of priors, including Gaussian priors, priors based on (truncated) random series, compound Poisson processes, and subordinators. We also investigate the limiting shape of the posterior distribution and derive a nonparametric version of the Bernstein-von Mises theorem for a specific class of priors on a function space with increasing parameter dimension. We show that the marginal posterior of the integral over $f$ does some automatic bias correction and contracts with a faster rate than the MLE. In this case, credible sets are also asymptotic confidence intervals. It is also shown that the frequentist coverage of credible sets is lost under model misspecification.