[Forum SIS] DEC Seminar - April 18th / A. van der Vaart (Leiden University)

[Catia Scricciolo]

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                    STATISTICS SEMINAR SERIES - BOCCONI UNIVERSITY
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The Department of Decision Sciences, Bocconi University, cordially invites 
all interested to attend the following seminar:

 
Speaker: Aad van der Vaart, Leiden University
Title: Nonparametric credible sets
Date: April 18th, 2013
Time: 12:30 pm
Venue: Room 3-E4-SR03, Via Roentgen 1, Milano

 

Abstract

In the past decades Bayesian nonparametric methods have developed into a success story, 
first in practice and in the last ten years also backed up by theory. The theory mostly 
concerned contraction rates of posterior distributions in a frequentist-Bayes framework, 
where the Bayesian model defines the posterior distribution, but the data are assumed to 
have been generated from a fixed distribution. The general highlight is that posterior 
distributions in nonparametric problems such as density or regression function estimation 
can contract to a given truth at the frequentist optimal rate of recovery. A hierarchical 
Bayesian framework can even deliver this when the regularity of the parameter is unknown 
(so-called adaptation). A question is whether there are equally comforting conclusions about 
uncertainty quantification through a nonparametric posterior distribution. Is the spread in 
the posterior (or the lack of spread), possibly measured by a credible set, a good basis for 
expressing estimation error? Recent results show that Bayesian oversmoothing, by specifying 
a prior that models the parameters as more regular than it really is, can have disastrous 
consequences. The big question concerns the performance of hierarchical Bayesian procedures 
(or the closely related empirical Bayesian ones). The matter is complicated by the fact that 
non-Bayesian confidence sets also may run into trouble, not only in a philosophical sense, 
but in practice.
 



For more information on the DEC statistics seminar series, please visit
http://www.unibocconi.eu/statseminar












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Catia Scricciolo 
Department of Decision Sciences 
"L. Bocconi" University 
Via G. Röntgen 1 
(Room 3-E1-07) 
I-20136 Milano (ITALY) 

Tel.:     +39 02 58365684 
Fax:      +39 02 58365630 
E-mail:   catia.scricciolo a unibocconi.it 
Webpage:  http://faculty.unibocconi.eu/catiascricciolo/ 
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