  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.
