Appropriate basis selection based on Bayesian inference for analyzing measured data reflecting photoelectron wave interference

TL;DR

This paper introduces a Bayesian inference method for selecting the optimal basis in EXAFS data analysis, enabling robust extraction of physical parameters and RDF without relying on traditional FEFF analysis.

Contribution

The study presents a Bayesian inference approach that automatically selects the best basis for EXAFS analysis and estimates physical parameters directly from signals.

Findings

Advanced Fourier basis is optimal for EXAFS regression.

Robust estimation of Debye-Waller factor achieved.

RDF can be extracted solely from EXAFS signals.

Abstract

In this study, we applied Bayesian inference for extended X-ray absorption fine structure (EXAFS) to select an appropriate basis from among Fourier, wavelet and advanced Fourier bases, and we extracted a radial distribution function (RDF) and physical parameters from only EXAFS signals using physical prior knowledge, which is to be realized in general in condensed systems. To evaluate our method, the well-known EXAFS spectrum of copper was used for the EXAFS data analysis. We found that the advanced Fourier basis is selected as an appropriate basis for the regression of the EXAFS signal in a quantitative way and that the estimation of the Debye-Waller factor can be robustly realized only by using the advanced Fourier basis. Bayesian inference based on minimal restrictions allows us to not only eliminate some unphysical results but also select an appropriate basis. Generally, FEFF analysis is used for estimating physical parameters such as Deby-Waller and extracting RDF. Bayesian inference enables us to simultaneously select an appropriate basis and optimized physical parameters without FEFF analysis, which results in extracting RDF from only EXAFS signals. These advantages lead to the general usage of Bayesian inference for EXAFS data analysis.