Statistical Issues in Astrophysical Searches for Particle Dark Matter

TL;DR

This review discusses statistical challenges in astrophysical dark matter searches, emphasizing the importance of likelihood methods, handling nuisance parameters, and comparing frequentist and Bayesian approaches.

Contribution

It provides a comprehensive overview of statistical issues specific to dark matter detection, highlighting the role of likelihood techniques and the treatment of uncertainties.

Findings

Likelihood approach enhances sensitivity of dark matter searches.

Nuisance parameters are degenerate with parameters of interest.

Frequentist methods dominate hypothesis testing, Bayesian methods for parameter estimation.

Abstract

In this review statistical issues appearing in astrophysical searches for particle dark matter, i.e. indirect detection (dark matter annihilating into standard model particles) or direct detection (dark matter particles scattering in deep underground detectors) are discussed. One particular aspect of these searches is the presence of very large uncertainties in nuisance parameters (astrophysical factors) that are degenerate with parameters of interest (mass and annihilation/decay cross sections for the particles). The likelihood approach has become the most powerful tool, offering at least one well motivated method for incorporation of nuisance parameters and increasing the sensitivity of experiments by allowing a combination of targets superior to the more traditional data stacking. Other statistical challenges appearing in astrophysical searches are to large extent similar to any new physics search, for example at colliders, a prime example being the calculation of trial factors. Frequentist methods prevail for hypothesis testing and interval estimation, Bayesian methods are used for assessment of nuisance parameters and parameter estimation in complex parameter spaces. The basic statistical concepts will be exposed, illustrated with concrete examples from experimental searches and caveats will be pointed out.