# Adaptive optimal scaling of Metropolis–Hastings algorithms using the Robbins–Monro process

*P. H. Garthwaite*,
*Y. Fan* and
*S. A. Sisson*

*Communications in Statistics - Theory and Methods*, 2016, vol. 45, issue 17, 5098-5111

**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. Based on theoretical considerations we give a simple estimator of this constant for Gaussian proposal distributions. The effectiveness of our method is demonstrated with both simulated and real data examples.

**Date:** 2016

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**Persistent link:** https://EconPapers.repec.org/RePEc:taf:lstaxx:v:45:y:2016:i:17:p:5098-5111

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**DOI:** 10.1080/03610926.2014.936562

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