Type: Seminar

Distribution: World

Expiry: 27 Aug 2010

Auth: uri@purix (assumed)

Scott Sisson School of Mathematics and Statistics University of New South Wales Location: Carslaw 173 Time: 2pm Friday, August 27, 2010 Title: Adaptive optimal scaling of Metropolis-Hastings algorithms Abstract: In Metropolis-Hastings algorithms it is common to manually adjust the scaling parameter of the proposal distribution so that the sampler achieves a reasonable overall acceptance probability. Some theoretical results suggest that the overall acceptance probability should be around 0.44 for univariate and 0.234 for multivariate proposal distributions. However, manually tuning the scaling parameter(s) to obtain this can be time-consuming, and impractical in high dimensions. I’ll present an adaptive method for the automatic scaling of Random-Walk Metropolis-Hastings algorithms. This method will adaptively update the scaling parameter of the proposal distribution to achieve a pre-sepecified overall acceptance probability. Our approach relies on the use of the Robbins-Monro search process, whose performance is determined by an unknown steplength constant, for which we give a very simple estimator. I’ll demonstrate how to incorporate the Robbins-Monro process into Metropolis-Hastings algorithms and demonstrate its effectiveness through simulated and real data examples. The algorithm is a quick robust method for finding the scaling parameter that yields a specified acceptance probability.