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SUMMARY:When Bayesians Can't Handle the Truth - Cosma Shalizi\, Carnegie M
 ellon University
DTSTART:20130201T160000Z
DTEND:20130201T170000Z
UID:TALK42437@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:There are elegant results on the consistency of Bayesian updat
 ing\nfor well-specified models facing IID or Markovian data\, but both com
 pletely\ncorrect models and fully observed states are vanishingly rare.  I
 n this\ntalk\, I give conditions for posterior convergence that hold when 
 the prior\nexcludes the truth\, which may have complex dependencies. The k
 ey dynamical\nassumption is the convergence of time-averaged log likelihoo
 ds\n(Shannon-McMillan-Breiman property). The main statistical assumption i
 s a\nbuilding into the prior a form of capacity control related to the met
 hod of\nsieves. With these\, I derive posterior and predictive convergence
 \, and a\nlarge deviations principle for the posterior\, even in infinite-
 dimensional\nhypothesis spaces\; and clarify role of the prior and of mode
 l averaging as\nregularization devices.\n\nPaper: http://projecteuclid.org
 /euclid.ejs/1256822130
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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