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SUMMARY:Frequentist coverage of adaptive nonparametric  Bayesian credible 
 sets - Botond Szabo (Eindhoven University of Technology)
DTSTART:20140203T110000Z
DTEND:20140203T120000Z
UID:TALK50651@talks.cam.ac.uk
CONTACT:Zoubin Ghahramani
DESCRIPTION:We investigate the frequentist coverage of Bayesian credible s
 ets\nin a nonparametric setting. We consider a scale of priors of varying\
 nregularity and choose the regularity by an empirical Bayes method.\nNext 
 we consider a central set of prescribed posterior probability\nin the post
 erior distribution of the chosen regularity.\nWe show that such an adaptiv
 e Bayes credible set gives correct\nuncertainty quantification of `polishe
 d tail' parameters\,\nin the sense of high probability of coverage of such
  parameters. On the negative\nside we show by theory and example that adap
 tation of the prior\nnecessarily leads to gross and haphazard uncertainty 
 quantification for\nsome true parameters that are still within the Sobolev
  regularity scale.\n\nThis is a joint work with Aad van der Vaart and Harr
 y van Zanten
LOCATION:Engineering Department\, CBL Room BE-438
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