Europhys. Lett.
Volume 76, Number 3, November 2006
Page(s) 353 - 359
Section General
Published online 29 September 2006
Europhys. Lett., 76 (3), pp. 353-359 (2006)
DOI: 10.1209/epl/i2006-10287-1

An adaptive Metropolis-Hastings scheme: Sampling and optimization

D. H. Wolpert1 and C. F. Lee2

1  NASA Ames Research Center - Mail Stop 269-1, Moffett Field, CA 94035-1000, USA
2  Physics Department, Clarendon Laboratory, Oxford University - Oxford OX1 3PU, UK

received 31 May 2006; accepted in final form 11 September 2006
published online 29 September 2006

We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field approximation to the target distribution, and update the proposal distribution to be that approximation. We employ our algorithm to sample the energy distribution for several spin-glasses and we demonstrate the superiority of our algorithm to the conventional MH algorithm in sampling and in annealing optimization.

02.70.Tt - Justifications or modifications of Monte Carlo methods.
05.10.Ln - Monte Carlo methods.
02.70.Uu - Applications of Monte Carlo methods.

© EDP Sciences 2006