Use of the profile likelihood function in searches for new physics

We describe likelihood-based statistical tests for use in high energy physicsfor the discovery of new phenomena and for construction of confidence intervals.Explicit formulae for the asymptotic distributions of test statistics based onthe profile likelihood ratio are derived using results of Wilks and Wald. Wemotivate and justify the use of a representative data set, called the " Asimovdata set " , which provides a simple method to obtain the median experimentalsensitivity of a search or measurement as well as fluctuations about thisexpectation.