Pierre E. Jacob on the 26th of February, 4p.m. - Unbiased MCMC with couplings

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sylvain.lecorff

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Jan 30, 2020, 7:12:15 AM1/30/20

to All About That Bayes

Dear all,

On Wednesday 26th of February at 4p.m., we will have the pleasure of welcoming Pierre E. Jacob, Associate Professor of Statistics at Harvard University (https://sites.google.com/site/pierrejacob/).

The talk will take place at AgroParisTech (16 rue Claude Bernard), room to be announced.

Title

Unbiased MCMC with couplings

Abstract

MCMC methods yield estimators that converge to integrals of interest in the limit of the number of iterations. This iterative asymptotic justification is not ideal; first, it stands at odds with current trends in computing hardware, with increasingly parallel architectures; secondly, the choice of "burn-in" or "warm-up" is arduous. This talk will describe recently proposed estimators that are unbiased for the expectations of interest while having a finite computing cost and a finite variance. They can thus be generated independently in parallel and averaged over. The method also provides practical upper bounds on the distance (e.g. total variation) between the marginal distribution of the chain at a finite step and its invariant distribution. The key idea is to generate "faithful" couplings of Markov chains, whereby pairs of chains coalesce after a random number of iterations. This talk will provide an overview of this line of research.

Main reference: https://arxiv.org/abs/1708.03625.

Code in R available at: https://github.com/pierrejacob/unbiasedmcmc.

All relevant information on the seminar may be found here: https://sites.google.com/view/all-about-that-bayes/