Estimating Convergence of Markov chains with L-Lag Couplings

Niloy Biswas; Pierre E. Jacob; Paul Vanetti

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arXiv · 1905.09971

Estimating Convergence of Markov chains with L-Lag Couplings

Niloy Biswas·Pierre E. Jacob·Paul Vanetti

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Abstract

Markov chain Monte Carlo (MCMC) methods generate samples that are asymptotically distributed from a target distribution of interest as the number of iterations goes to infinity. Various theoretical results provide upper bounds on the distance between the target and marginal distribution after a fixed number of iterations. These upper bounds are on a case by case basis and typically involve intractable quantities, which limits their use for practitioners. We introduce L-lag couplings to generate computable, non-asymptotic upper bound estimates for the total variation or the Wasserstein distance of general Markov chains. We apply L-lag couplings to the tasks of (i) determining MCMC burn-in, (ii) comparing different MCMC algorithms with the same target, and (iii) comparing exact and approximate MCMC. Lastly, we (iv) assess the bias of sequential Monte Carlo and self-normalized importance samplers.

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Niloy Biswas, Pierre E. Jacob, Paul Vanetti. 2019-10-28. Estimating Convergence of Markov chains with L-Lag Couplings. https://arxiv.org/abs/1905.09971

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