Composition analysis based on Bayesian methods

Abstract

In this work we test the most widely used methods for fitting the composition fraction in data, namely maximum likelihood, $\chi^2$, mean value of the distributions and mean value of the posterior probability function. We discuss the discrimination power of the four methods in different scenarios: signal to noise discrimination; two signals; and distributions of Xmax for mixed primary mass composition. We introduce a "distance" parameter, which can be used to estimate, as a rule of thumb, the precision of the discrimination. Finally, we conclude that the most reliable methods in all the studied scenarios are the maximum likelihood and the mean value of the posterior probability function.