Jiang Zhang, Wang Jin, Tirrell Matthew V, de Pablo Juan J, Chen Wei
X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL 60439, USA.
Materials Science Division, Argonne National Laboratory, Lemont, IL 60439, USA.
J Synchrotron Radiat. 2022 May 1;29(Pt 3):721-731. doi: 10.1107/S1600577522003034. Epub 2022 Apr 22.
Bayesian-inference-based approaches, in particular the random-walk Markov Chain Monte Carlo (MCMC) method, have received much attention recently for X-ray scattering analysis. Hamiltonian MCMC, a state-of-the-art development in the field of MCMC, has become popular in recent years. It utilizes Hamiltonian dynamics for indirect but much more efficient drawings of the model parameters. We described the principle of the Hamiltonian MCMC for inversion problems in X-ray scattering analysis by estimating high-dimensional models for several motivating scenarios in small-angle X-ray scattering, reflectivity, and X-ray fluorescence holography. Hamiltonian MCMC with appropriate preconditioning can deliver superior performance over the random-walk MCMC, and thus can be used as an efficient tool for the statistical analysis of the parameter distributions, as well as model predictions and confidence analysis.
基于贝叶斯推理的方法，特别是随机游走马尔可夫链蒙特卡罗（MCMC）方法，近年来在X射线散射分析中受到了广泛关注。哈密顿量MCMC是MCMC领域的一项前沿进展，近年来已变得流行起来。它利用哈密顿动力学来间接但更有效地绘制模型参数。我们通过估计小角X射线散射、反射率和X射线荧光全息术中几种典型场景的高维模型，描述了用于X射线散射分析反演问题的哈密顿量MCMC原理。具有适当预处理的哈密顿量MCMC比随机游走MCMC具有更优越的性能，因此可作为参数分布统计分析、模型预测和置信度分析的有效工具。
