Abstract

. The `frequentist' approach to statistics, currently dominating statistical practice in astrophysics, is compared to the historically older Bayesian approach, which is now growing in popularity in other scientific disciplines, and which provides unique, optimal solutions to well-posed problems. The two approaches address the same questions with very different calculations, but in simple cases often give the same final results, confusing the issue of whether one is superior to the other. Here frequentist and Bayesian methods are applied to problems where such a mathematical coincidence does not occur, allowing assessment of their relative merits based on their performance, rather than on philosophical argument. Emphasis is placed on a key distinction between the two approaches: Bayesian methods, based on comparisons among alternative hypotheses using the single observed data set, consider averages over hypotheses; frequentist methods, in contrast, average over hypothetical alternative...

Citations