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

In this study, we applied Bayesian inference to extended X-ray absorption fine structure (EXAFS) to select an appropriate basis from Fourier, windowed Fourier, and advanced Fourier bases, and we extracted magnitude spectra obtained by these bases, which are closely related to local structure near the target atom. Based on our method, we also estimate optimal physical parameters incorporating prior physical knowledge; reasonable characteristics of noise superimposed on the analyzed data and of increasing coordination number with far distance in solid materials. To evaluate our method, the well-known EXAFS spectrum of copper was analyzed. We found that the advanced Fourier basis is an appropriate basis for the quantitative regression of the EXAFS signal and that the estimation of the Debye-Waller factor can be robustly realized by using the advanced Fourier basis. Bayesian inference based on minimal restrictions of prior knowledge allows us not only to eliminate some unphysical results but also to select an appropriate basis. Even in the absence of structural information, Bayesian inference enables us to simultaneously select the appropriate basis and optimize the physical parameters from the EXAFS signals. Bayesian inference can pave the way to more systematic and quantitative extraction of proximity structures from measured data in EXAFS analysis of real data. (author)