TY - JOUR A1 - Klebanov, Ilja A1 - Schuster, Ingmar T1 - Markov Chain Importance Sampling - a highly efficient estimator for MCMC T2 - Journal of Computational and Graphical Statistics N2 - Markov chain (MC) algorithms are ubiquitous in machine learning and statistics and many other disciplines. Typically, these algorithms can be formulated as acceptance rejection methods. In this work we present a novel estimator applicable to these methods, dubbed Markov chain importance sampling (MCIS), which efficiently makes use of rejected proposals. For the unadjusted Langevin algorithm, it provides a novel way of correcting the discretization error. Our estimator satisfies a central limit theorem and improves on error per CPU cycle, often to a large extent. As a by-product it enables estimating the normalizing constant, an important quantity in Bayesian machine learning and statistics. Y1 - 2020 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/8109 ER -