Université de Marne-la-Vallée,
Analyse et Mathématiques Appliquées,
5 Bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2,
France.
Abstract: 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.
Keywords: Hastings-Metropolis algorithm; inhomogeneous Markov chain; MCMC; nonparametric estimation; rate of convergence.
C. R. Acad. Sci. Paris, 2001, t. 333, Série I, p. 881-884.