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| 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 {\em 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. |
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