Titre: The Importance Markov Chain

Abstract: The Importance Markov chain is a new algorithm bridging the gap between rejection sampling and importance sampling, moving from one to the other through a tuning parameter. Based on a modified sample of an instrumental Markov chain targeting an instrumental distribution (typically with a MCMC kernel), the Importance Markov chain aims to construct an extended Markov chain where the marginal distribution of the first component converges to the target distribution. We obtain geometric ergodicity for this extended kernel as well as a law of large numbers and a central limit theorem, under mild assumptions on the instrumental kernel.