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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On applications of Empirical Bayes approaches to t
he Normal Means problem - Matthew Stephens (Univer
sity of Chicago)
DTSTART;TZID=Europe/London:20180625T140000
DTEND;TZID=Europe/London:20180625T144500
UID:TALK106960AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/106960
DESCRIPTION:The normal means problem is very simple: given nor
mally-distributed observations with known variance
s and unknown means\, estimate the means. That is\
, given \;X_j \\sim N(\\theta_j\, \\sigma_j^2\
, estimate \;\\theta_j. A key idea is that one
can do better than the maximum likelihood estimat
es\, \;\\hat{\\theta}_j= \\X_j\, in particular
by use of appropriate "shrinkage" estimators. One
attractive way to perform shrinkage estimation in
practice is to use Empirical Bayes methods. That
is\, to assume that \;\\theta_j \;are inde
pendent and identically distributed from some dist
ribution \;g \;that is to be estimated fro
m the data. Then\, given such an estimate \;\\
hat{g}\, the posterior distributions of \;\\th
eta_j \;can be computed to perform inference.
We call this the "Empirical Bayes Normal Means" (E
BNM) problem.
Despite its simplicity\
, solving the EBNM problem has a wide range of pra
ctical applications. Here we present some flexible
non-parametric approaches we have recently develo
ped for solving the EBNM problem\, and describe th
eir application to several different settings: fal
se discovery rate (FDR) estimation\, non-parametri
c smoothing\, and sparse matrix factorization prob
lems (ie sparse factor analysis and sparse princip
al components analysis).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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