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SUMMARY:MCMC Importance Sampling via Moreau-Yosida Envelopes - Dootika Vat
 s (None / Other)
DTSTART:20241127T112500Z
DTEND:20241127T121500Z
UID:TALK221542@talks.cam.ac.uk
DESCRIPTION:Markov chain Monte Carlo (MCMC) is the workhorse computational
  algorithm employed for inference&nbsp\;in&nbsp\;Bayesian statistics. Grad
 ient-based MCMC algorithms are known to yield faster converging Markov cha
 ins.&nbsp\;&nbsp\;In&nbsp\;modern parsimonious models\, the use of non-dif
 ferentiable priors is fairly standard\, yielding non-differentiable poster
 iors. Without differentiability\, gradient-based MCMC algorithms cannot be
  employed effectively. Recently proposed proximal MCMC approaches\, howeve
 r\, can partially remedy this limitation. These approaches employ the More
 au-Yosida (MY) envelope to smooth the nondifferentiable prior enabling sam
 pling from an approximation to the target posterior.&nbsp\;In&nbsp\;this w
 ork\, we leverage properties of the MY envelope to construct an importance
  sampling paradigm to correct for this approximation error. We establish a
 symptotic normality of the importance sampling estimators with an explicit
  expression for the asymptotic variance which we use to derive&nbsp\;a pra
 ctical metric of sampling efficiency. Numerical studies show that the prop
 osed scheme can yield lower variance estimators compared to existing proxi
 mal MCMC alternatives. This work is led by Apratim Shukla (IIT Kanpur) and
  in collaboration with Eric Chi (Rice University).
LOCATION:Seminar Room 1\, Newton Institute
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