Bayesian Inference on Hamiltonian Selections for M\"ossbauer Spectroscopy

TL;DR

This paper introduces a Bayesian inference method for analyzing M"ossbauer spectra, enabling more reliable hyperfine interaction selection and parameter estimation with confidence intervals, improving over traditional least-squares fitting.

Contribution

It presents a novel Bayesian spectral analysis approach that allows for Hamiltonian selection and parameter estimation with uncertainty quantification in M"ossbauer spectroscopy.

Findings

Bayesian free energy effectively selects the appropriate Hamiltonian.

Posterior distributions provide confidence intervals for parameters.

Analysis accuracy depends on noise intensity in numerical experiments.

Abstract

M\"ossbauer spectroscopy, which provides knowledge related to electronic states in materials, has been applied to various fields such as condensed matter physics and material sciences. In conventional spectral analyses based on least-square fitting, hyperfine interactions in materials have been determined from the shape of observed spectra. In conventional spectral analyses, it is difficult to discuss the validity of the hyperfine interactions and the estimated values. We propose a spectral analysis method based on Bayesian inference for the selection of hyperfine interactions and the estimation of M\"ossbauer parameters. An appropriate Hamiltonian has been selected by comparing Bayesian free energy among possible Hamiltonians. We have estimated the M\"ossbauer parameters and evaluated their estimated values by calculating the posterior distribution of each M\"ossbauer parameter with confidence intervals. We have also discussed the accuracy of the spectral analyses to elucidate the noise intensity dependence of numerical experiments.