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SUMMARY:Measuring Sample Discrepancy with Diffusions - Andrew Duncan (Univ
 ersity of Sussex\; The Alan Turing Institute)
DTSTART:20170718T144000Z
DTEND:20170718T152000Z
UID:TALK74021@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In many applications one often wishes to quantify the discrepa
 ncy between a sample and a target probability distribution. &nbsp\;This ha
 s become particularly relevant for Markov Chain Monte Carlo methods\, wher
 e practitioners are now turning to biased methods which trade off asymptot
 ic exactness for computational speed. &nbsp\;While a reduction in variance
  due to more rapid sampling can outweigh the bias introduced\, the inexact
 ness creates new challenges for parameter selection. &nbsp\;The natural me
 tric in which to quantify this discrepancy is the Wasserstein or Kantorovi
 ch metric. &nbsp\;However\, the computational difficulties in computing th
 is quantity has typically dissuaded practitioners. &nbsp\;&nbsp\;&nbsp\;To
  address this\, we introduce a new computable quality measure based on Ste
 in&#39\;s method that quantifies the maximum discrepancy between sample an
 d target expectations over a large class of test functions. &nbsp\;We demo
 nstrate this tool by comparing exact\, biased\, and deterministic sample s
 equences and illustrate applications to hyperparameter selection\, converg
 ence rate assessment\, and quantifying bias-variance tradeoffs in posterio
 r inference.  <br><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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