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CATEGORIES:Statistics
SUMMARY:General Bayesian updating and model misspecificati
on - Chris Holmes\, University of Oxford
DTSTART;TZID=Europe/London:20150508T160000
DTEND;TZID=Europe/London:20150508T170000
UID:TALK58611AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/58611
DESCRIPTION:Bayesian statistics provides a unified approach to
the updating of beliefs but is challenged by mode
rn applications through the formal requirement to
define the true sampling distribution\, or joint l
ikelihood\, for the whole data generating process
regardless of the study objective. So even if the
task is inference for a low-dimensional statistic
Bayesian analysis is required to model the complet
e data distribution and\, moreover\, assume that t
he model is ``true''. In this talk we present a co
herent procedure for general Bayesian inference ba
sed on the use of loss functions to connect inform
ation in data to parameters of interest. The updat
ing of a prior belief distribution to a posterior
then follows from a decision theoretic foundation
involving cumulative loss functions and a requirem
ent for coherency. Sensitivity to model misspecifi
cation can be characterised via neighbourhoods in
model space around the approximating model. Import
antly\, the procedure coincides with Bayesian upda
ting when a true likelihood is known\, yet provide
s coherent subjective inference in much more gener
al settings. We demonstrate the approach on exampl
es including model-free general Bayesian co-cluste
ring of time series.\n
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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