  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.
