Multiplicative scale uncertainties in the unified approach for constructing confidence intervals

TL;DR

This paper examines how uncertainties in detection efficiency influence 90% confidence intervals in the unified approach, showing that coverage remains proper and intervals expand smoothly with increasing efficiency uncertainty.

Contribution

It introduces a quantitative analysis of how Gaussian detection efficiency uncertainties affect confidence intervals in the unified approach, extending previous methods.

Findings

Confidence intervals maintain proper coverage despite efficiency uncertainties.

Interval widths increase quadratically with the relative uncertainty in efficiency.

Proper coverage is preserved over a wide range of signal strengths.

Abstract

We have investigated how uncertainties in the estimation of the detection efficiency affect the 90% confidence intervals in the unified approach for constructing confidence intervals. The study has been conducted for experiments where the number of detected events is large and can be described by a Gaussian probability density function. We also assume the detection efficiency has a Gaussian probability density and study the range of the relative uncertainties $\sigma_\epsilon$ between 0 and 30%. We find that the confidence intervals provide proper coverage over a wide signal range and increase smoothly and continuously from the intervals that ignore scale uncertainties with a quadratic dependence on $\sigma_\epsilon$.