What is the likelihood function, and how is it used in particle physics?

Abstract

Likelihood functions are ubiquitous in data analyses at the LHC and elsewhere in particle physics. Partly because "probability" and "likelihood" are virtual synonyms in everyday English, but crucially distinct in data analysis, there is great potential for confusion. Furthermore, each of various approaches to statistical inference (likelihoodist, Neyman-Pearson, Bayesian) uses the likelihood function in different ways. This note is intended to provide a brief introduction at the advanced undergraduate or beginning graduate student level, citing a few papers giving examples and containing numerous pointers to the vast literature on likelihood. The Likelihood Principle (routinely violated in particle physics analyses) is mentioned as an unresolved issue in the philosophical foundations of statistics.

arXiv comment9 pages, 3 figures

References in corpus (3)

• Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments
• Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC $pp$ collision data at $\sqrt{s}=$ 7 and 8 TeV
• Lectures on Statistics in Theory: Prelude to Statistics in Practice

Cited by in corpus (1)

• Publishing statistical models: Getting the most out of particle physics experiments