Statistics Seminar: Scott Sisson -- Adaptive optimal scaling of Metropolis-Hastings algorithms

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.