The Banff Challenge: Statistical Detection of a Noisy Signal

• Published in: Statistical science Vol. 23; no. 3; pp. 354 - 364
• Main Authors: Davison, A. C., Sartori, N.
• Format: Journal Article
• Language: English
• Published: Institute of Mathematical Statistics 01-08-2008; The Institute of Mathematical Statistics
• Subjects: Approximation; Bayesian inference; Confidence interval; Datasets; Frequentism; higher-order asymptotics; Inference; Large Hadron Collider; likelihood; Mathematical functions; Mathematical independent variables; noninformative prior; orthogonal parameter; P values; Parametric models; particle physics; Poisson distribution; Signal detection
• ISSN: 0883-4237; 2168-8745
• DOI: 10.1214/08-STS260

Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability model for this and derive frequentist and noninformative Bayesian procedures for inference about the signal. Both are highly accurate in realistic cases, with the frequentist procedure having the edge for interval estimation, and the Bayesian procedure yielding slightly better point estimates. We also argue that the significance, or p-value, function based on the modified likelihood root provides a comprehensive presentation of the information in the data and should be used for inference.