  In experiments that are aimed at detecting astrophysical sources such as
neutrino telescopes, one usually performs a search over a continuous parameter
space (e.g. the angular coordinates of the sky, and possibly time), looking for
the most significant deviation from the background hypothesis. Such a procedure
inherently involves a "look elsewhere effect", namely, the possibility for a
signal-like fluctuation to appear anywhere within the search range. Correctly
estimating the $p$-value of a given observation thus requires repeated
simulations of the entire search, a procedure that may be prohibitively
expansive in terms of CPU resources. Recent results from the theory of random
fields provide powerful tools which may be used to alleviate this difficulty,
in a wide range of applications. We review those results and discuss their
implementation, with a detailed example applied for neutrino point source
analysis in the IceCube experiment.
