Reference priors for high energy physics

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.

💡 Research Summary

The paper addresses a pervasive problem in high‑energy physics (HEP) analyses that rely on Bayesian inference: the choice of prior for parameters with little or no prior information is usually taken to be uniform, but such a choice is not invariant under re‑parameterisation and can even lead to improper posteriors. To overcome this, the authors advocate the use of reference priors, a rigorously defined class of priors that embody the principle of minimal informativeness. The construction of a reference prior proceeds from the Fisher information matrix of the statistical model; for a one‑dimensional parameter θ the reference density is proportional to the square root of the Fisher information, I(θ)½. This definition guarantees invariance under smooth transformations of θ, thereby removing the dependence of the posterior on the arbitrary choice of parameterisation.

The methodology is first applied to the canonical problem of measuring a production cross‑section σ. In a typical HEP counting experiment the observed event count n follows a Poisson distribution with mean μ = σ L ε + b, where L is the integrated luminosity, ε the detection efficiency, and b the known background. Assuming L and ε are known constants, the Fisher information for σ is I(σ) = L ε / (σ L ε + b). The corresponding reference prior is therefore πR(σ) ∝