  Hamiltonian Monte Carlo (HMC) algorithms which combine numerical
approximation of Hamiltonian dynamics on finite intervals with stochastic
refreshment and Metropolis correction are popular sampling schemes, but it is
known that they may suffer from slow convergence in the continuous time limit.
A recent paper of Bou-Rabee and Sanz-Serna (Ann. Appl. Prob., 27:2159-2194,
2017) demonstrated that this issue can be addressed by simply randomizing the
duration parameter of the Hamiltonian paths. In this article, we use the same
idea to enhance the sampling efficiency of a constrained version of HMC, with
potential benefits in a variety of application settings. We demonstrate both
the conservation of the stationary distribution and the ergodicity of the
method. We also compare the performance of various schemes in numerical studies
of model problems, including an application to high-dimensional covariance
estimation.
