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

Author

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

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.

Suggested Citation

  • P. H. Garthwaite & Y. Fan & S. A. Sisson, 2016. "Adaptive optimal scaling of Metropolis–Hastings algorithms using the Robbins–Monro process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(17), pages 5098-5111, September.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:17:p:5098-5111
    DOI: 10.1080/03610926.2014.936562
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    Cited by:

    1. David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2021. "Comparisons of Australian Mental Health Distributions," Monash Econometrics and Business Statistics Working Papers 12/21, Monash University, Department of Econometrics and Business Statistics.
    2. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2021. "Bayesian estimation for a semiparametric nonlinear volatility model," Economic Modelling, Elsevier, vol. 98(C), pages 361-370.

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