# Bayesian Hamiltonian Selection in X-ray Photoelectron Spectroscopy

## TL;DR

This paper introduces an automated Bayesian approach for selecting and parameterizing effective Hamiltonians in core-level XPS spectra analysis, improving accuracy and providing uncertainty quantification.

## Contribution

The paper presents a novel Bayesian model selection framework using exchange Monte Carlo sampling for automatic Hamiltonian selection and parameter estimation in XPS spectra analysis.

## Key findings

- Successfully applied to Ce and La compounds' 3d XPS spectra
- Confirmed the method's selections align with physical knowledge
- Enabled uncertainty evaluation of the estimated parameters

## Abstract

Core-level X-ray photoelectron spectroscopy (XPS) is a useful measurement technique for investigating the electronic states of a strongly correlated electron system. Usually, to extract physical information of a target object from a core-level XPS spectrum, we need to set an effective Hamiltonian by physical consideration so as to express complicated electron-to-electron interactions in the transition of core-level XPS, and manually tune the physical parameters of the effective Hamiltonian so as to represent the XPS spectrum. Then, we can extract physical information from the tuned parameters. In this paper, we propose an automated method for analyzing core-level XPS spectra based on the Bayesian model selection framework, which selects the effective Hamiltonian and estimates its parameters automatically. The Bayesian model selection, which often has a large computational cost, was carried out by the exchange Monte Carlo sampling method. By applying our proposed method to the 3$d$ core-level XPS spectra of Ce and La compounds, we confirmed that our proposed method selected an effective Hamiltonian and estimated its parameters appropriately; these results were consistent with conventional knowledge obtained from physical studies. Moreover, using our proposed method, we can also evaluate the uncertainty of its estimation values and clarify why the effective Hamiltonian was selected. Such information is difficult to obtain by the conventional analysis method.