Advice on describing Bayesian analysis of neutron and X-ray reflectometry

Abstract

As a result of the availability of modern software and hardware, Bayesian analysis is becoming more popular in neutron and X-ray reflectometry analysis. The understandability and replicability of these analyses may be harmed by inconsistencies in how the probability distributions central to Bayesian methods are represented in the literature. Herein advice is provided on how to report the results of Bayesian analysis as applied to neutron and X-ray reflectometry. This includes the clear reporting of initial starting conditions, the prior probabilities, the results of any analysis and the posterior probabilities that are the Bayesian equivalent of the error bar, to enable replicability and improve understanding. It is believed that this advice, grounded in the authors' experience working in the field, will enable greater analytical reproducibility in the work of the reflectometry community, and improve the quality and usability of results.

Interfacial spin structures in Pt/Tb3Fe5O12 bilayer films on Gd3Yadav, Bake, Lee et al. 2023Phys. Rev. MaterialsSelf Cite1000View full textAdd to dashboardCite

“…There is considerable uncertainty for the small Pt magnetization, as discussed later. The best-fit parameters are shown in Table I, and later, an analysis of the uncertainty in the parameters is given using Monte Carlo sampling [37,38]. To facilitate comparison with magnetometry, we have also converted the magnetic SLD value into a magnetization using the standard coefficient relating the magnetic SLD and volume magnetization: C = 2.91 × 10 −9 Å −2 cm 3 /emu [39].…”

“…As the magnetic structure is relatively complex with two distinct "spinterfaces," and the Pt moment is relatively weak, it is worthwhile using advanced fitting methods to assess the correlation and uncertainty in all of the fitting parameters. To this end, the Monte Carlo Markov chain (MCMC) sampling method [38] is a powerful technique to perform Bayesian analysis. The principle is to analyze how the fitting residual (χ 2 ) varies for sets of parameters sampled randomly in parameter space, computing the log-likelihood, based on the prior and posterior probabilities.…”

On the interactions between RNA and titrateable lipid layers: implications for RNA delivery with lipid nanoparticles

“…Bayesian analysis was performed using Markov chain Monte Carlo (MCMC) sampling to estimate the posterior probability distributions for each fit parameter, which were used to discuss if the fit is sensitive to this fit parameter and if parameters are correlated. 39 The data for the lipid layers alone were fit using multiple models, which were compared based upon the calculated global χ 2 ( i.e. the total for the 3 contrasts) and Bayesian distributions ( i.e.…”

Epitaxial graphene growth on cubic silicon carbide on silicon with high temperature neutron reflectometry: an operando study

“…Each parameter in each layer is varied within physically relevant limits along with background using a differential evolution algorithm until the fitted data matches the experimental data with a minimized χ 2 value. Once a good fit with the differential evolution algorithm is achieved the fits were repeated using a Markov chain Monte Carlo (MCMC) 24 routine using 2000 steps, 200 walkers, and a thinning of 1 yielding a total of 2000 fits. This results in a spread of possible fits 12 and the reported values are the median values for each variable parameter from this spread and the error is the standard deviation.…”