Markov chain Monte Carlo methods such as Gibbs sampling and simple forms of
the Metropolis algorithm typically move about the distribution being sampled
via a random walk. For the complex, high-dimensional distributions commonly
encountered in Bayesian inference and statistical physics, the distance moved
in each iteration of these algorithms will usually be small, because it is
difficult or impossible to transform the problem to eliminate dependencies
between variables. The inefficiency inherent in taking such small steps is
greatly exacerbated when the algorithm operates via a random walk, as in such a
case moving to a point n steps away will typically take around n^2 iterations.
Such random walks can sometimes be suppressed using ``overrelaxed'' variants of
Gibbs sampling (a.k.a. the heatbath algorithm), but such methods have hitherto
been largely restricted to problems where all the full conditional
distributions are Gaussian. I present an overrelaxed Markov chain Monte Carlo
algorithm based on order statistics that is more widely applicable. In
particular, the algorithm can be applied whenever the full conditional
distributions are such that their cumulative distribution functions and inverse
cumulative distribution functions can be efficiently computed. The method is
demonstrated on an inference problem for a simple hierarchical Bayesian model.Comment: uuencoded compressed postscript (with instructions on decoding