An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift
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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.
KeywordsAdaptive Markov Chain Monte Carlo Langevin algorithms Metropolis-Hastings algorithms Stochastic approximation algorithms
AMS 2000 Subject Classification65C05 65C40 60J27 60J35
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- C. Andrieu, and Y. F. Atchade, “On the efficiency of adaptive MCMC algorithms,” Technical Report 1, 2005.Google Scholar
- C. Andrieu, and E. Moulines, “On the ergodicity properties of some adaptive MCMC algorithms,” to appear Annals of Applied Probability, 2005.Google Scholar
- A. Benveniste, M. Métivier, and P. Priouret, “Adaptive algorithms and stochastic approximations,” In Applications of Mathematics, Springer: Paris-New York, 1990.Google Scholar
- L. Breyer, M. Piccioni, and S. Scarlatti, “Optimal scaling of MALA for nonlinear regression,” Technical Report, 2002.Google Scholar
- M. Metivier, and P. Priouret, “Application of Kushner and Clark lemma to general classes of stochastic algorithms,” IEEE-IT vol. 30, 1984.Google Scholar
- G. O. Roberts, and J. S. Rosenthal, “Optimal scaling of various Metropolis-Hastings algorithms,” Statistical Science vol. 16, 2001.Google Scholar
- J. S. Rosenthal, and G. O. Roberts, “Coupling and Ergodicity of adaptive MCMC,” Technical Report, MCMC preprints, 2005.Google Scholar