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.

翻译：汉密尔顿·蒙特卡洛(HMC)算法将汉密尔顿动态的定时数字近似值与歇斯底里补充和大都会校正相结合,这些算法是流行的抽样办法,但众所周知,它们可能因连续时限缓慢趋同而受到影响,布拉比和桑兹-塞纳(Ann. Appl.Prob., 27:2159-2194, 2017)的最新论文表明,这一问题可以通过简单地随机排列汉密尔顿道的长度参数来解决。在本条中,我们使用同样的想法来提高受限制的HMC的取样效率,在各种应用环境中都有潜在好处。我们既可以证明对固定分布的保护,也可以证明该方法的灵敏性。我们还比较了模型问题数字研究中各种办法的绩效,包括对高维可变性估计的应用。