[Statlist] seminar on statistics

[Christina Kuenzli]

              ETH and University of Zurich 

                           Proff. 
         A.D. Barbour - P. Buehlmann - F. Hampel 
              H.R. Kuensch - S. van de Geer

***********************************************************    
    We are pleased to announce the following talk
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April 21, Friday, 15.15 h,   LEO C 15
    
Inconsistency of Bayes and MDL under Misspecification   
     
Peter Grünwald,  CWI, Amsterdam/EURANDOM, Eindhoven  

We show that Bayesian and MDL inference can be statistically
inconsistent under misspecification: for any a > 0, there exists a
distribution P, a set of distributions (model) M, and a 'reasonable'
prior on M such that
(a) P is not in M (the model is wrong)
(b) There is a distribution P' in M with KL-divergence D(P,P') = a

yet, if data are i.i.d. according to P, then the Bayesian posterior
concentrates on an (ever-changing) set of distributions that all have
KL-divergence to P much larger than a. If the posterior is used for
classification purposes, it can even perform worse than random
guessing.

The result is fundamentally different from existing Bayesian
inconsistency results due to Diaconis, Freedman and Barron, in that we
can choose the model M to be only countably large; if M were
well-specified (`true'), then by Doob's theorem this would immediately
imply consistency.

Joint work with John Langford of the Toyota Technological Institute,
Chicago.

________________________________________________________
Christina Kuenzli            <kuenzli at stat.math.ethz.ch>
Seminar fuer Statistik      
Leonhardstr. 27,  LEO D11      phone: +41 (0)44 632 3438         
ETH-Zentrum,                   fax  : +41 (0)44 632 1228 
CH-8092 Zurich, Switzerland        http://stat.ethz.ch/~