Markov Chain Monte Carlo Methods and Some Attempts at Parallelizing Them

IDS.190 – Topics in Bayesian Modeling and Computation

Abstract:

MCMC methods yield approximations that converge to quantities of interest in the limit of the number of iterations. This iterative asymptotic justification is not ideal: it stands at odds with current trends in computing hardware. Namely, it would often be computationally preferable to run many short chains in parallel, but such an approach is flawed because of the so-called “burn-in” bias.  This talk will first describe that issue and some known resolutions, including regeneration techniques and sequential Monte Carlo samplers.  Then I will describe a recent proposal, joint work with John O’Leary, Yves Atchadé and others, that allows to completely remove the burn-in bias. In a nutshell, the proposed unbiased estimators are constructed from pairs of chains, that are generated over a random, finite number of iterations. Furthermore, their variances and costs can be made arbitrarily close to those of standard MCMC estimators, if desired.  The proposed method is described in https://arxiv.org/abs/1708.03625 and code in R is available to reproduce the experiments at https://github.com/pierrejacob/unbiasedmcmc.

Biography:

Pierre E. Jacob is an Associate Professor of Statistics at Harvard University.  He develops methods for statistical inference, e.g. to run Monte Carlo methods on parallel computers, to compare models, to estimate latent variables, and to deal with intractable likelihood functions.

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For more information and an up-to-date schedule, please see https://stellar.mit.edu/S/course/IDS/fa19/IDS.190/

**Taking IDS.190 satisfies the seminar requirement for students in MIT’s Interdisciplinary Doctoral Program in Statistics (IDPS), but formal registration is open to any graduate student who can register for MIT classes. And the meetings are open to any interested researcher.   Talks will be followed by 30 minutes of tea/snacks and informal discussion.**