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