Article

Methodology and Computing in Applied Probability

, Volume 8, Issue 2, pp 235-254

First online:

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

  • Yves F. AtchadéAffiliated withDepartment of Mathematics and Statistics, University of Ottawa Email author 

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Abstract

This paper extends some adaptive schemes that have been developed for the Random Walk Metropolis algorithm to more general versions of the Metropolis-Hastings (MH) algorithm, particularly to the Metropolis Adjusted Langevin algorithm of Roberts and Tweedie (1996). Our simulations show that the adaptation drastically improves the performance of such MH algorithms. We study the convergence of the algorithm. Our proves are based on a new approach to the analysis of stochastic approximation algorithms based on mixingales theory.

Keywords

Adaptive Markov Chain Monte Carlo Langevin algorithms Metropolis-Hastings algorithms Stochastic approximation algorithms

AMS 2000 Subject Classification

65C05 65C40 60J27 60J35