Adaptive Sticky Generalized Metropolis

We introduce a new class of adaptive Metropolis algorithms called adaptive sticky algorithms for efficient general-purpose simulation from a target probability distribution. The transition of the Metropolis chain is based on a multiple-try scheme and the different proposals are generated by adaptive nonparametric distributions. Our adaptation strategy uses the interpolation of support points from the past history of the chain as in the adaptive rejection Metropolis. The algorithm efficiency 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. Despite the algorithms are presented for univariate target distributions, we show that they can be easily extended to the multivariate context by a Gibbs sampling strategy. We show the ergodicity of the proposed algorithms and illustrate their efficiency and effectiveness through some simulated examples involving target distributions with complex structures.