Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process
Abstract
We present an adaptive method for the automatic scaling of Random-Walk Metropolis-Hastings algorithms, which quickly and robustly identifies the scaling factor that yields a specified overall sampler acceptance probability. Our method relies on the use of the Robbins-Monro search process, whose performance is determined by an unknown steplength constant. We give a very simple estimator of this constant for proposal distributions that are univariate or multivariate normal, together with a sampling algorithm for automating the method. The effectiveness of the algorithm is demonstrated with both simulated and real data examples. This approach could be implemented as a useful component in more complex adaptive Markov chain Monte Carlo algorithms, or as part of automated software packages.
Keywords
Cite
@article{arxiv.1006.3690,
title = {Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process},
author = {P. H. Garthwaite and Y. Fan and S. A. Sisson},
journal= {arXiv preprint arXiv:1006.3690},
year = {2010}
}