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SUMMARY:The Correlated Pseudo-Marginal Method - Arnaud Doucet (University 
 of Oxford)
DTSTART:20170706T131500Z
DTEND:20170706T140000Z
UID:TALK73177@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Joint work with George Deligiannidis and Michael Pitt<br><a ta
 rget="_blank" rel="nofollow"><span><br>The pseudo-marginal algorithm is a 
 popular Metropolis&ndash\;Hastings-type scheme which samples asymptoticall
 y from a target probability density when we are only able to estimate unbi
 asedly an unnormalised version of it. However\, for the performance of thi
 s scheme not to degrade as the number   T   of data points increases\, it 
 is typically necessary for the number   N   of Monte Carlo samples to be p
 roportional to     T      to control the relative variance of the likeliho
 od ratio estimator appearing in the acceptance probability of this algorit
 hm. The correlated pseudo-marginal algorithm is a modification of the pseu
 do-marginal method using a likelihood ratio estimator computed using two c
 orrelated likelihood estimators. For random effects models\, we show under
  regularity conditions that the parameters of this scheme can be selected 
 such that the relative variance of this likelihood ratio estimator is cont
 rolled when   N   increases sublinearly with   T   and we provide guidelin
 es on how to optimise the parameters of the algorithm based on a non-stand
 ard weak convergence analysis. The efficiency of computations for Bayesian
  inference relative to the pseudo-marginal method empirically increases wi
 th   T   and is higher than two orders of magnitude in some of our example
 s. </span> </a><a target="_blank" rel="nofollow">   </a><br>
LOCATION:Seminar Room 1\, Newton Institute
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