Markov Chain Importance Sampling—A Highly Efficient Estimator for MCMC

Markov chain algorithms are ubiquitous in machine learning and statistics many other disciplines. Typically, these can be formulated as acceptance rejection methods. In this work, we present a novel estimator applicable to methods, dubbed importance sampling, which efficiently makes use of rejected proposals. For the unadjusted Langevin algorithm, it provides way correcting discretization error. Our satisfies central limit theorem improves on error per CPU cycle, often large extent. As by-product enables estimating normalizing constant, an important quantity Bayesian statistics. Supplementary materials for article available online.