Parameter estimation for X-ray scattering analysis with Hamiltonian Markov Chain Monte Carlo

Zhang Jiang, Jin Wang, Matthew V. Tirrell, Juan J. De Pablo, Wei Chen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)721-731
Number of pages11
JournalJournal of Synchrotron Radiation
Volume29
DOIs
StatePublished - May 1 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 International Union of Crystallography. All rights reserved.

Keywords

  • Markov chain Monte Carlo
  • X-ray reflectivity
  • small-angle X-ray scattering

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