Nonparametric Bayes for support boundary recovery

In support boundary recovery we observe a Poisson point process on the epigraph of an unknown function f. The statistical problem is to recover the boundary f from the data. In this model, the nonparametric MLE exists for many parameter spaces but leads to suboptimal rates for estimation of functionals. This motivates to study a Bayesian approach. We derive a non-standard limiting shape result for a compound Poisson process prior and a function space with increasing parameter dimension. It is shown that the marginal posterior of the integral of f performs an automatic bias correction and contracts with a faster rate than the MLE . As a negative result, it is shown that the frequentist coverage of credible sets is lost for linear functions indicating that credible sets only have frequentist coverage for priors that are specifically constructed to match properties of the underlying true function. (Joint work with Markus Reiss, Berlin).

• Speaker: Johannes Schmidt-Hieber, University of Leiden
• Friday 19 October 2018, 16:00–17:00
• Venue: MR12.
• Series: Statistics; organiser: Dr Sergio Bacallado.