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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Zero-Variance Hamiltonian MCMC - Mira\, A (Univers
ity of Lugano)
DTSTART;TZID=Europe/London:20140513T140000
DTEND;TZID=Europe/London:20140513T150000
UID:TALK52562AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52562
DESCRIPTION:Interest is in evaluating\, by Markov chain Monte
Carlo (MCMC) simulation\, the expected value of a
function with respect to a\, possibly unnormalized
\, probability distribution.\nA general purpose va
riance reduction technique for the MCMC estimator
\, based on the zero-variance principle introduced
in the physics literature\, is proposed.\nThe mai
n idea is to construct control variates based on t
he score function.\nConditions for asymptotic unbi
asedness of the zero-variance estimator are derive
d. A central limit theorem is also proved under re
gularity conditions.\nThe potential of the zero-va
riance strategy is illustrated with real applicati
ons to probit\, logit and GARCH Bayesian models.
\nThe Zero-Variance principle is efficiently combi
ned with Hamiltonian Monte Carlo and Metropolis ad
justed Langevin algorithms without exceeding the c
omputational requirements since its main ingredien
t (namely the score function) is exploited twice:
once to guide the Markov chain towards relevant po
rtion of the state space via a clever proposal\, t
hat exploits the geometry of the target and achiev
es convergence in fewer iterations\, and then to p
ost-process the simulated path of the chain to red
uce the variance of the resulting estimators.\n\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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