An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift

Abstract

This paper proposes an adaptive version for the Metropolis adjusted Langevin algorithm with a truncated drift (T-MALA). The scale parameter and the covariance matrix of the proposal kernel of the algorithm are simultaneously and recursively updated in order to reach the optimal acceptance rate of 0:574 (see Roberts and Rosenthal (2001)) and to estimate and use the correlation structure of the target distribution. We develop some convergence results for the algorithm. A simulation example is presented.Markov Chain Monte Carlo, Stochastic approximation algorithms, Metropolis Adjusted Langevin algorithm, geometric rate of convergence.