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SUMMARY:Bayesian optimality and frequentist extended admissibility are equ
 ivalent in saturated models - Daniel Roy (University of Toronto)
DTSTART:20161215T110000Z
DTEND:20161215T120000Z
UID:TALK69212@talks.cam.ac.uk
CONTACT:Louise Segar
DESCRIPTION:For finite parameter spaces under finite loss\, every Bayesian
  procedure derived from a prior with full support is admissible\, and ever
 y admissible procedure is Bayes. This relationship begins to break down as
  we move to continuous parameter spaces. Under some regularity conditions\
 , admissible procedures can be shown to be the limits of Bayesian procedur
 es. Under additional regularity\, they are generalized Bayesian\, i.e.\, t
 hey minimize the Bayes risk with respect to an improper prior. In both the
 se cases\, one must venture beyond the strict confines of Bayesian analysi
 s. Using methods from mathematical logic and nonstandard analysis\, we int
 roduce the class of nonstandard Bayesian decision procedures---namely\, th
 ose whose Bayes risk with respect to some prior is within an infinitesimal
  of the optimal Bayes risk.  Without any regularity conditions\, we show t
 hat a decision procedure is extended admissible if and only if its nonstan
 dard extension is nonstandard Bayes. We apply the nonstandard theory to de
 rive a purely standard theorem: on a compact parameter space\, every exten
 ded admissible estimator is Bayes if the risk function is continuous.\n\nJ
 oint work with Haosui Duanmu.
LOCATION:CBL Room BE-438\, Department of Engineering
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