In this paper, T. J. Loredo explains the Bayesian approach to probability and argues that it offers a more coherent framework for scientific inference than the traditional frequentist interpretation of statistics. Bayesian probability treats probability as a measure of uncertainty and uses prior knowledge together with new data to update beliefs through Bayes’ theorem. The paper outlines the mathematical foundations of Bayesian inference and shows how it can be used for parameter estimation and comparing competing models. These concepts are illustrated through astrophysical examples, including detecting weak signals in noisy data and analyzing the small number of neutrinos observed from supernova SN 1987A. The work highlights how Bayesian methods can provide clearer reasoning and more consistent conclusions when scientists must draw inferences from limited or uncertain data.

https://bayes.wustl.edu/gregory/articles.pdf