Bayesian data analysis tools for atomic physics

TL;DR

This paper introduces Bayesian data analysis methods tailored for atomic physics, demonstrating their application through spectral analysis examples and providing a computational tool called Nested fit.

Contribution

It presents practical Bayesian analysis techniques for atomic spectra, including model comparison and probability distribution calculations, with a new software implementation.

Findings

Bayesian methods effectively distinguish spectral features.

Nested fit software facilitates spectral model analysis.

Probabilistic spectrum modeling without unique solutions.

Abstract

We present an introduction to some concepts of Bayesian data analysis in the context of atomic physics. Starting from basic rules of probability, we present the Bayes' theorem and its applications. In particular we discuss about how to calculate simple and joint probability distributions and the Bayesian evidence, a model dependent quantity that allows to assign probabilities to different hypotheses from the analysis of a same data set. To give some practical examples, these methods are applied to two concrete cases. In the first example, the presence or not of a satellite line in an atomic spectrum is investigated. In the second example, we determine the most probable model among a set of possible profiles from the analysis of a statistically poor spectrum. We show also how to calculate the probability distribution of the main spectral component without having to determine uniquely the spectrum modeling. For these two studies, we implement the program Nested fit to calculate the different probability distributions and other related quantities. Nested fit is a Fortran90/Python code developed during the last years for analysis of atomic spectra. As indicated by the name, it is based on the nested algorithm, which is presented in details together with the program itself.