Hybrid Monte-Carlo: A little-known MCMC algorithm

Speaker: Alex Beskos (University College London)

Time: 3:00PM
Date: Thu 18th February 2010

Location: Statistics Seminar Room- Library building

We are interested in the behavior of MCMC algorithms in high dimensions. Results in the literature have shown that the 'vanilla' Random Walk Metropolis scales as 1/n, with n being the dimension of the state space. The so-called Metropolis-adjusted Langevin algorithm scales as 1/n^{1/3}, as it uses information about the gradient of the target density. We consider an MCMC algorithm popular amongst physicists (but not statisticians): the Hybrid Monte-Carlo (HMC) algorithm. HMC scales as 1/n^{1/4}. In connection with related results for other MCMC algorithms, for a simple class of target distributions we identify a single asymptotically optimal acceptance probability for HMC (which is 0.651, to three decimal places) irrespectively of the particular selection of target distribution.

(This talk is part of the Statistics and Actuarial Science series.)