Estimating the significance of a signal in a multi-dimensional search

TL;DR

This paper reviews how random field theory can be used to efficiently estimate the significance of signals in multi-dimensional searches, reducing computational costs in astrophysical experiments like neutrino detection.

Contribution

It introduces the application of random field theory to estimate p-values in multi-dimensional searches, exemplified by neutrino point source analysis in IceCube.

Findings

Random field theory provides a powerful framework for significance estimation.

Implementation reduces computational resources needed for search analyses.

Application to IceCube demonstrates practical effectiveness.

Abstract

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.