Clopper-Pearson Bounds from HEP Data Cuts

TL;DR

This paper extends classical Clopper-Pearson confidence bounds to high-energy physics data with cuts, providing a computational tool useful for Higgs search analyses.

Contribution

It generalizes Clopper-Pearson bounds to scenarios with data cuts and offers a practical Fortran program for confidence interval calculation.

Findings

Provides rigorous confidence bounds for signal probability with data cuts.

Offers a web-accessible Fortran program for confidence bounds calculation.

Applicable to Higgs search data analysis at LEP.

Abstract

For the measurement of $N_s$ signals in $N$ events rigorous confidence bounds on the true signal probability $p_{\rm exact}$ were established in a classical paper by Clopper and Pearson [Biometrica 26, 404 (1934)]. Here, their bounds are generalized to the HEP situation where cuts on the data tag signals with probability $P_s$ and background data with likelihood $P_b<P_s$. The Fortran program which, on input of $P_s$, $P_b$, the number of tagged data $N^Y$ and the total number of data $N$, returns the requested confidence bounds as well as bounds on the entire cumulative signal distribution function, is available on the web. In particular, the method is of interest in connection with the statistical analysis part of the ongoing Higgs search at the LEP experiments.