Bayesian methods for error analysis in XAFS measurements

MAXIMILIANO RIDDICK; ENRIQUE E. ÁLVAREZ; LEANDRO ANDRINI

Campinas (Virtual)

Otro; Annual Users Meeting LNLS/CNPEM; 2021

LNLS/CNPEM

Given the standard formulae of XAFS, it is usual separate the parameters in theoretical (known) and obtained from experimental data (unknown).Several methods are developed aiming to estimate the unknown parameters. The objective of our work is present a brief review of the standard classical procedures of these estimators,and analyze and discuss the methods with Bayesian techniques implemented.The standard procedures focuses on least square estimation, and are based on linearization and approximation algorithms implementing Fourier or Wavelet transform. Krappe and Rossner [1] proposed a Bayesian approach following the Bayes-Turchin model, in which the prior selected follows a Normal distribution, where the variance-covariance matrix is diagonal. Rehr et.al[2]. suggest a more general implementation on XAS models. Our focus is detail the advantages and drawbacks/limitations of this approach.According to the conclusions, we suggest a few modifications in order to offer more generality and flexibility to the Bayesian implementation.References:[1] Krappe, H. J., & Rossner, H. H. (2000). Error analysis of XAFS measurements. Physical Review B, 61(10), 6596.[2] Rehr, J. J., Kozdon, J., Kas, J., Krappe, H. J., & Rossner, H. H. (2005). Bayes?Turchin approach to XAS analysis. Journalof synchrotron radiation, 12(1), 70-74.