Luca Martino (Universidad Carlos III de Madrid): Adaptive sticky Metropolis

In order to draw from univariate target densities, in the last decades several adaptive Monte Carlo techniques have been developed using an approach that approximates adaptively the target distribution. The most famous methodologies in this area, are probably the adaptive rejection sampling (ARS) and the adaptive rejection Metropolis sampling (ARMS). However, in literature have been introduced many other algorithms in which the proposal density is built using an interpolation procedure. In this work, we introduce a novel and simple adaptive Metropolis-Hasting algorithm based on this idea. Moreover, the algorithm is strengthened by a step that controls the evolution of the set of support points. This extra stage improves the computational cost and accelerates the convergence of the proposal distribution to the target. The performance of this novel approach are illustrated through numerical example, and some extensions are discussed.