Asymptotic formulae for estimating statistical significance in particle physics analyses

Within the framework of likelihood-based statistical tests for high energy physics measurements, we derive generalized expressions estimating significance discovery using asymptotic approximations Wilks and Wald a variety measurement models. These models include arbitrary numbers signal regions, control Gaussian constraints. We extend our to use representative or "Asimov" dataset proposed by Cowan et al. such that they are made data-free. While many complicated often involve solving systems coupled, multivariate equations, show these reduce closed-form results under simplifying assumptions. also validate predicted toy-based data in select cases.