Bayesian data analysis tools for atomic physics

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.

References in corpus (7)

• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• Bayes in the sky: Bayesian inference and model selection in cosmology
• A statistical test for Nested Sampling algorithms
• Bayesian Calibrated Significance Levels Applied to the Spectral Tilt and Hemispherical Asymmetry
• Measurement of the charged pion mass using X-ray spectroscopy of exotic atoms
• Bayesian inference of a negative quantity from positive measurement results
• Measurement of the charged pion mass using a low-density target of light atoms

Cited by in corpus (10)

• Nested sampling for physical scientists
• Nested Sampling Methods
• New Test of Modulated Electron Capture Decay of Hydrogen-Like ${}^{142}$Pm Ions: Precision Measurement of Purely Exponential Decay
• Mean shift cluster recognition method implementation in the nested sampling algorithm
• The Nested_fit data analysis program
• Line shape analysis of the K$\beta$ transition in muonic hydrogen
• Nested Sampling for Exploring Lennard-Jones Clusters
• Bayesian and Monte Carlo approaches to estimating uncertainty for the measurement of the bound-state $\beta$ decay of ${}^{205}{\mathrm{Tl}}^{81+}$
• Probing the partition function for temperature-dependent potentials with nested sampling
• A Bayesian Approach for Strong Field QED Tests with He-like Ions