The Hamiltonian Monte Carlo (HMC) method allows sampling from continuous densities. Favorable scaling with dimension has led to wide adoption of HMC by the statistics community. Modern auto-differentiating software should allow more widespread usage in Bayesian inverse problems. This paper analyzes the two major difficulties encountered using HMC for inverse problems: poor conditioning and multi-modality. Novel results on preconditioning and replica exchange Monte Carlo parameter selection are presented in the context of spectroscopy. Recommendations are analyzed rigorously in the Gaussian case, and shown to generalize in a fusion plasma reconstruction.

翻译：Hamiltonian Monte Carlo (HMC) 方法允许连续密度进行取样, 随规模的扩大而使统计界广泛采用HMC。 现代的自动区分软件应该允许在巴伊西亚反面问题中更广泛地使用HMC。 本文分析了在反面问题中使用HMC(HMC)遇到的两大困难: 机能差和多式问题。 Monte Carlo 参数选择的先决条件和复制交换的新结果在光谱中作了介绍。 在Gaussian 案中对建议进行了严格分析,并展示了在聚变等离子体重建中的一般化。