Estimating the "look elsewhere effect" when searching for a signal

The "look elsewhere effect" refers to a common situation where one searchesfor a signal in some space of parameters-for example, a resonance search withunknown mass, or a search for astrophysical point sources with unknown locationin the sky. Since Wilks' theorem does not apply in such cases, one usually hasto resort to computationally expansive Monte-Carlo simulations in order tocorrectly estimate the significance of a given observation. Recent results fromthe theory of random fields provide powerful tools which may be used toalleviate this difficulty, in a wide range of applications. We review thoseresults and discuss their implementation in problems of practical interest.