 If certain regularity conditions are met, then a general likelihood function will become a Gaussian function in the large sample limit.In such case the CLs upper limit at confidence level formula_2 (derived from the uniformly most powerful test) is given by

where formula_78 is the standard normal cumulative distribution, formula_79 is the maximum likelihood estimator of formula_21 and formula_81 is its standard deviation; the latter might be estimated from the inverse of the Fisher information matrix or by using the "Asimov" data set.This result happens to be equivalent to a Bayesian credible interval if a uniform prior for formula_21 is used.