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SUMMARY:Validating approximate Bayesian computation on posterior convergen
 ce - Wentao Li (Lancaster University)
DTSTART:20170705T084500Z
DTEND:20170705T093000Z
UID:TALK73153@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-author: Paul Fearnhead		(Lancaster University)       
  <br></span><br>Many statistical applications involve models for which it 
 is difficult to evaluate the likelihood\, but relatively easy to sample fr
 om. Approximate Bayesian computation is a likelihood-free method for imple
 menting Bayesian inference in such cases. We present a number of surprisin
 gly strong asymptotic results for the regression-adjusted version of appro
 ximate Bayesian Computation introduced by Beaumont et al. (2002). We show 
 that for an appropriate choice of the bandwidth in approximate Bayesian co
 mputation\, using regression-adjustment will lead to a posterior that\, as
 ymptotically\, correctly quantifies uncertainty. Furthermore\, for such a 
 choice of bandwidth we can implement an importance sampling algorithm to s
 ample from the posterior whose acceptance probability tends to 1 as we inc
 rease the data sample size. This compares favourably to results for standa
 rd approximate Bayesian computation\, where the only way to obtain its pos
 terior that correctly quantifies uncertainty is to choose a much smaller b
 andwidth\, for which the acceptance probability tends to 0 and hence for w
 hich Monte Carlo error will dominate. <br><br>Related Links<ul><li><a targ
 et="_blank" rel="nofollow" href="http://www-old.newton.ac.uk/cgi/https%3A%
 2F%2Farxiv.org%2Fabs%2F1609.07135">https://arxiv.org/abs/1609.07135</a></l
 i><li><a target="_blank" rel="nofollow" href="http://www-old.newton.ac.uk/
 cgi/https%3A%2F%2Farxiv.org%2Fabs%2F1506.03481">https://arxiv.org/abs/1506
 .03481</a></li></ul>
LOCATION:Seminar Room 1\, Newton Institute
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