Algorithmes de Hastings–Metropolis en interaction

We propose an adaptive MCMC method consisting of a set of parallel but non-Markovian and non i.i.d. discrete time processes, where each marginal uses the Hastings–Metropolis dynamic based on proposal densities depending on the other processes and learning from their past. We prove the geometric convergence of each marginal with a rate a.s. better than any arbitrary independent Hastings–Metropolis algorithm.