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SUMMARY:Multilevel sequential Monte Carlo Samplers. - Dr Ajay Jasra\, Nati
 onal University of Singapore
DTSTART:20150528T140000Z
DTEND:20150528T150000Z
UID:TALK58691@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:In this talk we consider the approximation of expectations w.r
 .t. probability distributions associated to the solution of partial differ
 ential equations (PDEs)\; this scenario appears routinely in Bayesian inve
 rse problems. In practice\, one often has to solve the associated PDE nume
 rically\, using\, for instance finite element methods and leading to a dis
 cretisation bias\, with the step-size level h_L. In addition\, the expecta
 tion cannot be computed analytically and one often resorts to Monte Carlo 
 methods. In the context of this problem\, it is known that the introductio
 n of the multilevel Monte Carlo (MLMC) method can reduce the amount of com
 putational effort to estimate expectations\, for a given level of error. T
 his is achieved via a telescoping identity associated to a Monte Carlo app
 roximation of a sequence of probability distributions. In many practical p
 roblems of interest\, one cannot achieve an i.i.d. sampling of the associa
 ted sequence of probability distributions. A sequential Monte Carlo (SMC) 
 version of the MLMC method is introduced to deal with this problem. It is 
 shown that under appropriate assumptions\, the attractive property of a re
 duction of the amount of computational effort to estimate expectations\, f
 or a given level of error\, can be maintained within the SMC context.  Thi
 s is a joint work with Alex Beskos (UCL)\, Kody Law (KAUST)\, Raul Tempone
  (KAUST) and Yan Zhou (NUS).\n\n*BIO*: Ajay Jasra received his PhD degree 
 in statistics from Imperial College London in 2005.\nSince 2011 he has bee
 n tenured associate professor at the Department of Statistics and Applied 
 Probability at the National University of Singapore. Between 2005-2008 he 
 has held various post-doctoral positions at the University of Oxford\, Uni
 versity of Cambridge and the Institute of Statistical Mathematics in Tokyo
 . He was also Chapman Fellow of Mathematics at Imperial College London in 
 that period. Between 2008-2011 he was assistant professor at Imperial Coll
 ege London. He is currently associate editor at Statistics and Computing\,
  American Journal of Algorithms and Computing and Stat and has over 60 pub
 lications.\n\n
LOCATION:LR5\, Department of Engineering
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