  We analyzed the X-ray photoemission spectra (XPS) of carbon 1s states in
graphene and oxygen-intercalated graphene grown on SiC(0001) using Bayesian
spectroscopy. To realize highly accurate spectral decomposition of the XPS
spectra, we proposed a framework for discovering physical constraints from the
absence of prior quantified physical knowledge, in which we designed the prior
probabilities based on the found constraints and the physically required
conditions. This suppresses the exchange of peak components during replica
exchange Monte Carlo iterations and makes possible to decompose XPS in the case
where a reliable structure model or a presumable number of components is not
known. As a result, we have successfully decomposed XPS of one monolayer (1ML),
two monolayers (2ML), and quasi-freestanding 2ML (qfs-2ML) graphene samples
deposited on SiC substrates with the meV order precision of the binding energy,
in which the posterior probability distributions of the binding energies were
obtained distinguishably between the different components of buffer layer even
though they are observed as hump and shoulder structures because of their
overlapping.
