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CATEGORIES:Machine Learning @ CUED
SUMMARY:Challenges in implementing the Bayesian paradigm -
Prof. Steve MacEachern (Ohio State)
DTSTART;TZID=Europe/London:20110310T120000
DTEND;TZID=Europe/London:20110310T130000
UID:TALK30214AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/30214
DESCRIPTION:The optimality properties of Bayesian inference ar
e well established\, and yet there remains a wide
gulf between the mathematical foundations of the m
ethods and practical implementation. The gap show
s up most strongly in specification of the prior d
istribution\, particularly when the analyst has (o
r wishes to inject) little information about the p
arameters. In such cases\, the prior distribution
often depends on the data itself\, and this depen
dence is routinely ignored in the subsequent analy
sis. In this talk\, we formalize the notion of a
data dependent prior distribution and show how to
bring the analysis into agreement with Bayes Theor
em. Properties of the adjustment are described\,
and a range of impacts on posterior inference is i
llustrated. The impact is particularly large in h
igh and infinite dimensional settings\, such as th
ose characterizing nonparametric Bayesian inferenc
e. In this high-dimensional setting\, a quick des
cription of the need for additional adjustments to
traditional Bayesian concepts such as the Bayes f
actor will be given. \n\nThe work on data depende
nt prior distributions is joint with Bill Darniede
r\; that on Bayes factors is joint with Xinyi Xu\,
Pingbo Lu\, and Ruoxi Xu. \n
LOCATION:Engineering Department\, CBL Room 438
CONTACT:Zoubin Ghahramani
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