Reference priors for high energy physics

TL;DR

This paper introduces a methodology for constructing parametrization-invariant, minimally informative priors in high energy physics Bayesian analysis, improving the robustness and interpretability of posterior inferences.

Contribution

It presents the reference analysis methodology for creating objective priors that are invariant under reparametrization, with practical applications to cross section measurements.

Findings

The methodology produces sensible, robust posterior distributions.

Application to top quark cross section measurement demonstrates practical utility.

Provides a mathematically rigorous way to choose priors in high energy physics.

Abstract

Bayesian inferences in high energy physics often use uniform prior distributions for parameters about which little or no information is available before data are collected. The resulting posterior distributions are therefore sensitive to the choice of parametrization for the problem and may even be improper if this choice is not carefully considered. Here we describe an extensively tested methodology, known as reference analysis, which allows one to construct parametrization-invariant priors that embody the notion of minimal informativeness in a mathematically well-defined sense. We apply this methodology to general cross section measurements and show that it yields sensible results. A recent measurement of the single top quark cross section illustrates the relevant techniques in a realistic situation.