BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Zero-Variance Hamiltonian MCMC - Mira\, A (University of Lugano)
DTSTART:20140513T130000Z
DTEND:20140513T140000Z
UID:TALK52562@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Interest is in evaluating\, by Markov chain Monte Carlo (MCMC)
  simulation\, the expected value of a function with respect to a\, possibl
 y unnormalized\, probability distribution.\nA general purpose variance red
 uction technique  for the MCMC estimator\, based on the zero-variance prin
 ciple introduced in the physics literature\, is proposed.\nThe main idea i
 s to construct control variates based on the score function.\nConditions f
 or asymptotic unbiasedness of the zero-variance estimator are derived. A c
 entral limit theorem is also proved under regularity conditions.\nThe pote
 ntial of the zero-variance strategy is illustrated with real applications 
 to  probit\, logit and GARCH  Bayesian models.\nThe Zero-Variance principl
 e is efficiently combined with Hamiltonian Monte Carlo and Metropolis adju
 sted Langevin algorithms without exceeding the computational requirements 
 since its main ingredient (namely the score function) is exploited twice: 
 once to guide the Markov chain towards relevant portion of the state space
  via a clever proposal\, that exploits the geometry of the target and achi
 eves convergence in fewer iterations\, and then to post-process the simula
 ted path of the chain to reduce the variance of the resulting estimators.\
 n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
END:VEVENT
END:VCALENDAR