Bayes and Frequentism: a particle physicist’s perspective
In almost every scientific field, an experiment involves collecting data and then analysing it. The analysis stage will often consist in trying to extract some physical parameter and estimating its uncertainty; this is known as Parameter Determination. An example would be the determination of the mass of the top quark, from data collected from high energy proton–proton collisions. A different aim is to choose between two possible hypotheses. For example, are data on the recession speed s of distant galaxies proportional to their distance d, or do they fit better to a model where the expansion of the Universe is accelerating? There are two fundamental approaches to such statistical analyses – Bayesian and Frequentist. This article discusses the way they differ in their approach to probability, and then goes on to consider how this affects the way they deal with Parameter Determination and Hypothesis Testing. The examples are taken from everyday life and from Particle Physics.