Searching for new phenomena with profile likelihood ratio tests

Likelihood ratio tests are standard statistical tools used in particle physics to perform tests of hypotheses. The null distribution of the likelihood ratio test statistic is often assumed to be χ², following Wilks’ theorem. However, in many circumstances relevant to modern experiments this theorem is not applicable. In this Expert Recommendation, we overview practical ways to identify these situations and provide guidelines on how to construct valid inference. We use examples from particle physics, but the statistical constructs discussed here can be used in any scientific discipline that relies on data analysis.