December, 2010
While adaptive methods for MCMC are under active development, their utility has been under-recognized. We briefly review some theoretical results relevant to adaptive MCMC. We then suggest a very simple and effective algorithm to adapt proposal densities for random walk Metropolis and Metropolis adjusted Langevin algorithms. The benefits of this algorithm are immediate, and we demonstrate its power by comparing its performance to that of three commonly-used MCMC algorithms that are widely-believed to be extremely efficient. Compared to data augmentation for probit models, slice sampling for geostatistical models, and Gibbs sampling with adaptive rejection sampling, the adaptive random walk Metropolis algorithm that we suggest is both more efficient and more flexible.
Keywords: adaptive, Markov chain Monte Carlo, Metropolis algorithm, Nonconjugate priors.
The manuscript is available in PDF format.