A Hasting-Metropolis algorithm with learning proposal

We present a non-homogeneous Hastings-Metropolis algorithm for which the pr oposal density approximates the target density, as the number of iterations increases. The proposal at the n-th step is a non-parametric estimate of t he density of the algorithm, and uses an increasing number of i.i.d. copies of the Markov chain. The resulting algorithm converges (in n) geometricall y faster than a Hastings-Metropolis algorithm with an arbitrary proposal. ( C) Academie des Sciences/Elsevier, Paris.