Open AccessParameter estimation for X‐ray scattering analysis with Hamiltonian Markov Chain Monte Carlo
Author(s) -
Jiang Zhang,
Wang Jin,
Tirrell Matthew V.,
de Pablo Juan J.,
Chen Wei
Publication year - 2022
Publication title -
journal of synchrotron radiation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.172
H-Index - 99
ISSN - 1600-5775
DOI - 10.1107/s1600577522003034
Subject(s) - markov chain monte carlo , hybrid monte carlo , statistical physics , markov random field , hamiltonian (control theory) , markov chain , scattering , random walk , monte carlo method , bayesian inference , bayesian probability , computer science , inference , physics , random field , metropolis–hastings algorithm , algorithm , mathematics , artificial intelligence , mathematical optimization , statistics , quantum mechanics , machine learning , segmentation , image segmentation
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.