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SUMMARY:Measuring sample quality with diffusions - Sebastian Vollmer (Oxfo
 rd)
DTSTART:20161125T160000Z
DTEND:20161125T170000Z
UID:TALK67491@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:Standard Markov chain Monte Carlo diagnostics\, like effective
  sample size\, are ineffective for biased sampling procedures that sacrifi
 ce asymptotic correctness for computational speed. Recent work addresses t
 his issue for a class of strongly log-concave target distributions by cons
 tructing a computable discrepancy measure based on Stein’s method that p
 rovably determines convergence to the target. We generalize this approach 
 to cover any target with a fast-coupling Ito diffusion by bounding the der
 ivatives of Stein equation solutions in terms of Markov process coupling r
 ates. As example applications\, we develop computable and convergence-dete
 rmining diffusion Stein discrepancies for log-concave\, heavy-tailed\, and
  multimodal targets and use these quality measures to select the hyperpara
 meters of biased samplers\, compare random and deterministic quadrature ru
 les\, and quantify bias-variance tradeoffs in approximate Markov chain Mon
 te Carlo. Our explicit multivariate Stein factor bounds may be of independ
 ent interest.\nPreprint: https://arxiv.org/abs/1611.06972
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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