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arXiv · 1006.3690

Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process

P. H. Garthwaite·Y. Fan·S. A. Sisson
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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.

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P. H. Garthwaite, Y. Fan, S. A. Sisson. 2010-06-18. Adaptive Optimal Scaling of Metropolis-Hastings Algorithms Using the Robbins-Monro Process. https://arxiv.org/abs/1006.3690

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