Title: Adaptive Sticky Generalized Metropolis
Abstract: In the last decades, several adaptive Markov Chain Monte Carlo (MCMC) techniques have been developed using proposal densities that approximate adaptively the target distribution. Moreover, different approaches have been proposed to update a proposal density within a MCMC algorithm.
Here, we focus on the construction of sequence of proposals via interpolation procedures, using a subset of previous generated samples. The first and the most famous methodology of this kind is surely the adaptive rejection Metropolis sampling (ARMS). A control test, checking the choice of interpolation points, must be added within the MCMC method to ensure the ergodicity of the chain and keep bounded the computational cost. We discuss different possibilities, advantages and drawbacks of this strategy, within different possible structures of MCMC methods.