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Pierre Jacob, Harvard University

22 May 2020 @ 12:00 - 13:30


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22 May 2020
12:00 - 13:30
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Academic Events

“Unbiased Markov chain Monte Carlo with couplings”


Various tasks in statistics involve numerical integration, for which Markov chain Monte Carlo (MCMC) methods are state-of-the-art. 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. (joint work with John O’Leary, Yves Atchadé)

The main reference has just appeared here: https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/rssb.12336