Shape and Satellite Studies of Highly Charged Ions X-ray Spectra Using Bayesian Methods

High-accuracy spectroscopy commonly requires dedicated investigation into the choice of spectral line modelling to avoid the introduction of unwanted systematic errors. For such a kind of problem, the analysis of χ2 and likelihood are normally implemented to choose among models. However, these standard practices are affected by several problems and, in the first place, they are useless if there is no clear indication in favour of a specific model. Such issues are solved by Bayesian statistics, in the context of which a probability can be assigned to different hypotheses, i.e., models, from the analysis of the same set of data. Model probabilities are obtained from the integration of the likelihood function over the model parameter space with the evaluation of the so-called Bayesian evidence. Here, some practical applications are presented within the context of the analysis of recent high-accuracy X-ray spectroscopy data of highly charged uranium ion transitions. The method to determine the most plausible profile is discussed in detail. The study of the possible presence of satellite peaks is also presented.