Deterministic dynamics is an essential part of many MCMC algorithms, e.g. Hybrid Monte Carlo or samplers utilizing normalizing flows. This paper presents a general construction of deterministic measure-preserving dynamics using autonomous ODEs and tools from differential geometry. We show how Hybrid Monte Carlo and other deterministic samplers follow as special cases of our theory. We then demonstrate the utility of our approach by constructing a continuous non-sequential version of Gibbs sampling in terms of an ODE flow and extending it to discrete state spaces. We find that our deterministic samplers are more sample efficient than stochastic counterparts, even if the latter generate independent samples.

翻译：确定性动态是许多MCMC算法的一个基本部分,例如混合蒙特卡洛或利用正常流流的取样员等。本文介绍了使用自主的代码和不同几何工具的确定性测量性动态的总体结构。我们展示了混合蒙特卡洛和其他确定性取样员如何作为我们理论的特殊案例加以遵循。然后,我们用ODE流来构建连续的非顺序版本的Gibbs采样方法,并将其扩展到离散的州空间,从而证明了我们的方法的效用。我们发现,我们的确定性采样员比对等样本更高效,即使后者产生独立的样本。