Application of Bayesian probability theory to the measurement of binomial data at past and future Tevatron experiments

Abstract

The experimental problem of converting a measured binomial quantity, the fraction of events in a sample that pass a cut, into a physical binomial quantity, the fraction of events originating from a signal source, is described as a system of linear equations. This linear system illustrates several familiar aspects of experimental data analysis. Bayesian probability theory is used to find a solution to this binomial measurement problem that allows for the straightforward construction of confidence intervals. This solution is also shown to provide an unbiased formalism for evaluating the behavior of data sets under different choices of cuts, including a cut designed to increase the significance of a possible, albeit previously unseen, signal. Several examples are used to illustrate the features of this method, including the discovery of the top quark and searches for new particles produced in association with $W^{\pm}$ bosons. It is also demonstrated how to use this method to make projections for the potential discovery of a Standard Model Higgs boson at a Tevatron Run 2 experiment, as well as the utility of measuring the integrated luminosity through inclusive $p\bar{p} \to W^{\pm}$ production.