Does waste-recycling really improve Metropolis-Hastings Monte Carlo algorithm?

Jean-François Delmas (1) , Benjamin Jourdain (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

The waste-recycling Monte Carlo (WR) algorithm, introduced by Frenkel, is a modification of the Metropolis-Hastings algorithm, which makes use of all the proposals, whereas the standard Metropolis-Hastings algorithm only uses the accepted proposals. We prove the convergence of the WR algorithm and its asymptotic normality. We give an example which shows that in general the WR algorithm is not asymptotically better than the Metropolis-Hastings algorithm : the WR algorithm can have an asymptotic variance larger than the one of the Metropolis-Hastings algorithm. However, in the particular case of the Metropolis-Hastings algorithm called Boltzmann algorithm, we prove that the WR algorithm is asymptotically better than the Metropolis-Hastings algorithm.

Mots clés: Metropolis-Hastings algorithm; Monte Carlo Markov chain; variance reduction; ergodic theorem; central limit theorem

Domaines: Probabilités [math.PR]

Jean-François Delmas, Benjamin Jourdain. Does waste-recycling really improve Metropolis-Hastings Monte Carlo algorithm?. 2006. ⟨hal-00117197v1⟩