Looking Elsewhere and Looking Everywhere (a.k.a. Multiple Testing ...

The Look Elsewhere Effect
One possible mathematical description is as follows:
Interested in detecting presence of a signal µ(xt), t = 1, . . . , T over a
discretised domain, {x1, . . . , xt}, on the basis of noisy measurements
This is to be detected against some known background, say 0.
Say, for the moment, that we are not specifically interested in
detecting the presence of the signal in some particular location xt, but
in detecting whether the a signal is present anywhere in the domain.
Formally:
as opposed to
Does there exist a t ∈ {1, . . . , T } such that µ(xt) = 0?
Is µ(xt) = 0 for some specific t ∈ {1, . . . , T }?
(but might also be interested in“for which t is µ(xt) = 0”)
Victor M. Panaretos (EPFL) Progress on Statistical Issues in Searches SLAC – June 2012 3 / 25