Séminaire Probabilités et Statistiques
Some methods based on couplings of Markov chain Monte Carlo algorithms
déc. 2021
Intervenant : Pierre Jacob
Institution : ESSEC Business School
Heure : 15h45 - 16h45
Lieu : 3L15

Markov chain Monte Carlo algorithms are commonly used to approximate a variety of probability distributions, such as posterior distributions arising in Bayesian analysis. I will review the idea of coupling in the context of Markov chains, and how this idea not only leads to theoretical analyses of Markov chains but also to new Monte Carlo methods. In particular, the talk will describe how coupled Markov chains can be used to obtain 1) unbiased estimators of expectations and normalizing constants, 2) non-asymptotic convergence diagnostics for Markov chains, and 3) unbiased estimators of the asymptotic variance of an MCMC ergodic average.

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