  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.
