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SUMMARY:Nonparametric Bayes for support boundary recovery - Johannes Schmi
 dt-Hieber\, University of Leiden
DTSTART:20181019T150000Z
DTEND:20181019T160000Z
UID:TALK109648@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:In support boundary recovery we observe a Poisson point proces
 s 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 ML
 E exists for many parameter spaces but leads to suboptimal rates for estim
 ation of functionals. This motivates to study a Bayesian approach. We deri
 ve a non-standard limiting shape result for a compound Poisson process pri
 or and a function space with increasing parameter dimension. It is shown t
 hat 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 r
 esult\, 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).
LOCATION:MR12
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