[Forum SIS] Bocconi DEC Seminar: Richard Nickl - April 14th

[Anna Simoni]

Dear colleagues,

The Department of Decision Sciences (DEC) of Bocconi University is pleased to invite you to the seminar:
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DEC Seminar
Università Bocconi
Room 3-E4-SR03
Via Rontgen 1 - 3rd floor
Time: 12:30pm

The DEC seminar schedule is available at http://www.unibocconi.eu/statseminar 

Thursday, April 14th

Richard Nickl
(University of Cambridge)

"A new approach to proving rates of contraction of posterior distributions in bayesian nonparametrics"

Abstract:

We develop a new approach to deriving rates of contraction for
nonparametric bayes procedures. While similar in spirit to the approach
taken in ghoshal, gosh, van der vaart (2000, AOS) and shen and wasserman
(2001, AOS), we propose a new approach to the nonparametric testing
problems employed in these proofs. We replace the Birge-Le Cam theory of
nonparametric hypothesis testing in Hellinger distance by a general
empirical process approach, that combines powerful concentration of measure 
phenomena of product measures -- in particular Talagrand's (1996, Invent. Math.)
 inequality -- with approximation theoretic properties of the support of the prior. 
This approach applies to many of the commonly used priors, such as Gaussian, 
Dirichlet etc, and can in particular be generalised to cover contraction results 
in general L^p-norms, 1 le p le infty, rather than only Hellinger or total variation 
distance. We discuss some apparent limitations of nonparametric bayes 
procedures that arise in L^p-loss for p>2, and some open conjectures related to it. 
[This is joint work with Evarist Gine.]

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Sincerely,
Anna Simoni

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Anna Simoni

Assistant Professor
Department of Decision Sciences
Università Bocconi
via Roentgen, 1
20136 Milano - Italy

Email:anna.simoni a unibocconi.it
Webpage: http://faculty.unibocconi.eu/annasimoni/