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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The Correlated Pseudo-Marginal Method - Arnaud Dou
cet (University of Oxford)
DTSTART;TZID=Europe/London:20170706T141500
DTEND;TZID=Europe/London:20170706T150000
UID:TALK73177AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/73177
DESCRIPTION:Joint work with George Deligiannidis and Michael P
itt
The pseudo-marginal algorithm is a popular Metrop
olis&ndash\;Hastings-type scheme which samples asy
mptotically from a target probability density when
we are only able to estimate unbiasedly an unnorm
alised version of it. However\, for the performanc
e of this scheme not to degrade as the number T
of data points increases\, it is typically neces
sary for the number N of Monte Carlo samples t
o be proportional to T to control the rel
ative variance of the likelihood ratio estimator a
ppearing in the acceptance probability of this alg
orithm. The correlated pseudo-marginal algorithm i
s a modification of the pseudo-marginal method usi
ng a likelihood ratio estimator computed using two
correlated likelihood estimators. For random effe
cts models\, we show under regularity conditions t
hat the parameters of this scheme can be selected
such that the relative variance of this likelihood
ratio estimator is controlled when N increase
s sublinearly with T and we provide guidelines
on how to optimise the parameters of the algorith
m based on a non-standard weak convergence analysi
s. The efficiency of computations for Bayesian inf
erence relative to the pseudo-marginal method empi
rically increases with T and is higher than tw
o orders of magnitude in some of our examples.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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