Practical Statistics for Particle Physics Analyses: Likelihoods (1/4)

<!--HTML-->This will be a 4-day series of 2-hour sessions as part of CERN's Academic Training Course. Each session will consist of a 1-hour lecture followed by one hour of practical computing, which will have exercises based on that day's lecture. While it is possible to follow just the lectures or just the computing exercises, we highly recommend that, because of the way this course is designed, participants come to both parts. In order to follow the hands-on exercises sessions, students need to bring their own laptops. The exercises will be run on a dedicated CERN Web notebook service, SWAN (swan.cern.ch), which is open to everybody holding a CERN computing account. The requirement to use the SWAN service is to have a CERN account and to have also access to Cernbox, the shared storage service at CERN. New users of cernbox are invited to activate beforehand cernbox by simply connecting to https://cernbox.cern.ch. A basic prior knowledge of ROOT and C++ is also recommended for participation in the practical session. Day 1: Likelihoods The likelihood approach is a very powerful method that can be used with individual events (i.e. does not require binning). Examples are given to make it plausible that the likelihood estimates of parameters are reasonable. Estimates of uncertainties in fitted parameters are discussed, and coverage is investigated. It is shown that the unbinned likelihood does not provide a measure of Goodness of Fit, although binned likelihood can.