  Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC)
method for performing approximate inference in complex probabilistic models of
continuous variables. In common with many MCMC methods, however, the standard
HMC approach performs poorly in distributions with multiple isolated modes. We
present a method for augmenting the Hamiltonian system with an extra continuous
temperature control variable which allows the dynamic to bridge between
sampling a complex target distribution and a simpler unimodal base
distribution. This augmentation both helps improve mixing in multimodal targets
and allows the normalisation constant of the target distribution to be
estimated. The method is simple to implement within existing HMC code,
requiring only a standard leapfrog integrator. We demonstrate experimentally
that the method is competitive with annealed importance sampling and simulating
tempering methods at sampling from challenging multimodal distributions and
estimating their normalising constants.
