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SUMMARY:Consensus-based sampling - Urbain Vaes (INRIA\, ENPC - École des 
 Ponts ParisTech\, INRIA Paris - Rocquencourt)
DTSTART:20220429T111500Z
DTEND:20220429T121500Z
UID:TALK171905@talks.cam.ac.uk
DESCRIPTION:In the first part of this talk\, I will present background mat
 erial on Bayesian inverse problems\, the associated challenges at the nume
 rical level\, and gradient-free sampling and optimization approaches for s
 olving them.&nbsp\; In the second part\, I will present recent work [1] on
  a novel gradient-free sampling method that is well suited for Bayesian in
 verse problems. The method is inspired by consensus-based methods in optim
 ization and based on a stochastic interacting particle system. We demonstr
 ate its potential in regimes where the target distribution is unimodal and
  close to Gaussian\; indeed we prove that it enables to recover a Laplace 
 approximation of the measure in certain parametric regimes and provide num
 erical evidence that this Laplace approximation attracts a large set of in
 itial conditions in a number of examples.\n&nbsp\;&nbsp\;&nbsp\; [1] https
 ://arxiv.org/abs/2106.02519
LOCATION:Seminar Room 1\, Newton Institute
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