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 autodifferentiating software should allow more widespread usage in Bayesian inverse problems. This paper analyzes two major difficulties encountered using HMC for inverse problems: poor conditioning and multimodality. Novel results on preconditioning and replica exchange Monte Carlo parameter selection are presented in the context of spectroscopy. Recommendations are given for the number of integration steps as well as step size, preconditioner type and fitting, annealing form, and schedule. These recommendations are analyzed rigorously in the Gaussian case and shown to generalize in a fusion plasma reconstruction.

中文翻译：

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反问题中的哈密顿蒙特卡罗。条件不佳和多式联运

Hamiltonian Monte Carlo (HMC) 方法允许从连续密度进行采样。有利的维度扩展导致统计界广泛采用 HMC。现代自微分软件应该允许在贝叶斯逆问题中更广泛地使用。本文分析了使用 HMC 解决逆问题时遇到的两个主要困难：条件差和多模态。在光谱学的背景下介绍了预处理和复制交换蒙特卡罗参数选择的新结果。给出了积分步骤数以及步长、预处理器类型和配件、退火形式和时间表的建议。在高斯情况下对这些建议进行了严格分析，并显示出在融合等离子体重建中的推广。