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We present an adaptive method for the automatic scaling of Random-WalkMetropolis-Hastings algorithms, which quickly and robustly identifies thescaling factor that yields a specified overall sampler acceptance probability.Our method relies on the use of the Robbins-Monro search process, whoseperformance is determined by an unknown steplength constant. We give a verysimple estimator of this constant for proposal distributions that areunivariate or multivariate normal, together with a sampling algorithm forautomating the method. The effectiveness of the algorithm is demonstrated withboth simulated and real data examples. This approach could be implemented as auseful component in more complex adaptive Markov chain Monte Carlo algorithms,or as part of automated software packages.

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