Estimation of Upper Limits Using a Poisson Statistic

TL;DR

This paper surveys various statistical methods for estimating upper limits in experiments with small event counts, introduces a new significance-based approach, and demonstrates its application through a toy model and a real particle decay search.

Contribution

It proposes a novel significance-based method for upper limit estimation in Poisson-distributed experiments, enhancing existing statistical techniques.

Findings

The new method effectively estimates upper limits using significance.

Application to a tau decay search demonstrates practical utility.

Comparison shows advantages over traditional event-count methods.

Abstract

Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a Poisson statistic. A new approach, based on the statistical significance of a signal rather than on the number of events in the signal region, is proposed. A toy model and an example of a recent search for the lepton number violating decay $\tau\to\mu\gamma$ are used to illustrate application of the discussed techniques.