  Hamiltonian Monte Carlo (HMC) is a powerful Markov Chain Monte Carlo (MCMC)
method for sampling from complex high-dimensional continuous distributions.
However, in many situations it is necessary or desirable to combine HMC with
other Metropolis-Hastings (MH) samplers. The common HMC-within-Gibbs strategy
implies a trade-off between long HMC trajectories and more frequent other MH
updates. Addressing this trade-off has been the focus of several recent works.
In this paper we propose Metropolis Augmented Hamiltonian Monte Carlo (MAHMC),
an HMC variant that allows MH updates within HMC and eliminates this trade-off.
Experiments on two representative examples demonstrate MAHMC's efficiency and
ease of use when compared with within-Gibbs alternatives.
