Spectral Analysis of X‐Ray Absorption Near Edge Structure in α‐Fe2O3 Based on Bayesian Spectroscopy

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A Bayesian spectroscopy technique is proposed to decompose weak pre‐edge structures from an X‐ray absorption near edge structure (XANES) spectrum. This methodology can perform model selection based on an information criterion of Bayes free energy. To explain the entire XANES spectrum measured at Fe K‐edge of α‐Fe2O3 with a partial fluorescence yield method, a phenomenological model of an absorption edge structure and plural Gaussian peak structures is introduced. The absorption edge structure is constructed by a step profile by an arctangent function and an accompanying peak by a pseudo‐Voigt function. As the result of model selection for estimating the number K of Gaussian components, it is found that the models of have posterior probabilities of the model selection. In these models, in spite of the number of Gaussian components being different, the pre‐edge structure is definitely decomposed to three components, and it is found that posterior probability distributions of the parameters for these components hardly change in these models (). This result shows that an appropriate spectral decomposition of the pre‐edge structure is realized. In addition, the robustness of such spectral decomposition is confirmed based on the evaluation of estimating accuracy of all spectral parameters by their posterior probability distributions.