  One of the most demanding calculations is to generate random samples from a
specified probability distribution (usually with an unknown normalizing
prefactor) in a high-dimensional configuration space. One often has to resort
to using a Markov chain Monte Carlo method, which converges only in the limit
to the prescribed distribution. Such methods typically inch through
configuration space step by step, with acceptance of a step based on a
Metropolis(-Hastings) criterion. An acceptance rate of 100% is possible in
principle by embedding configuration space in a higher-dimensional phase space
and using ordinary differential equations. In practice, numerical integrators
must be used, lowering the acceptance rate. This is the essence of hybrid Monte
Carlo methods. Presented is a general framework for constructing such methods
under relaxed conditions: the only geometric property needed is (weakened)
reversibility; volume preservation is not needed. The possibilities are
illustrated by deriving a couple of explicit hybrid Monte Carlo methods, one
based on barrier-lowering variable-metric dynamics and another based on
isokinetic dynamics.

Computational Physics;Computation