Including gaussian uncertainty on the background estimate for upper limit calculations using Poissonian sampling

TL;DR

This paper presents an analytic method to incorporate Gaussian background uncertainties into upper limit calculations with Poisson sampling, enabling faster computations in statistical analyses.

Contribution

It introduces a recursive polynomial-based likelihood expression for Gaussian uncertainties, improving computational efficiency in upper limit estimations.

Findings

Analytic likelihood expression derived for Gaussian background uncertainties.

Significant speed-up in upper limit calculations using Toy Monte Carlo.

Applicable when Gaussian assumption on background uncertainty is valid.

Abstract

A procedure to include the uncertainty on the background estimate for upper limit calculations using Poissonian sampling is presented for the case where a Gaussian assumption on the uncertainty can be made. Under that hypothesis an analytic expression of the likelihood is derived which can be written in terms of polynomials defined by recursion. This expression may lead to a significant speed up of computing applications that extract the upper limits using Toy Monte Carlo.