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

• Published in: Communications in statistics. Theory and methods Vol. 45; no. 17; pp. 5098 - 5111
• Main Authors: Garthwaite, P. H., Fan, Y., Sisson, S. A.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 01-09-2016; Taylor & Francis Ltd
• Subjects: Adaptive algorithms; Adaptive sampling; Algorithms; Bayesian analysis; Estimators; Markov analysis; Markov chain Monte Carlo; Monte Carlo simulation; Optimal scaling; Optimization; random-walk Metropolis-Hastings; Robbins-Monro; Samplers; Scaling; Statistics
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2014.936562

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.