Response to Comment from Robert Cousins on Confidence intervals for the Poisson distribution

TL;DR

This paper responds to a comment on confidence intervals for the Poisson distribution, defending the inclusion of non-physical parameter values in likelihood calculations for descriptive statistics.

Contribution

It clarifies the debate on whether non-physical parameter values should be included in likelihood-based confidence intervals for Poisson statistics.

Findings

Including non-physical values can be useful for descriptive statistics.

The author defends the methodological choice against the comment.

The discussion clarifies best practices in constructing confidence intervals.

Abstract

Robert Cousins has posted a comment on my manuscript on ``Confidence intervals for the Poisson distribution''. His key point is that one should not include in the likelihood non-physical parameter values, even for frequency statistics. This is my response, in which I contend that it can be useful to do so when discussing such descriptive statistics.