Systematic Errors

To introduce the ideas of statistical and systematic errors, this review first describes a simple pendulum experiment. We follow with a brief discussion of the Bayesian and frequentist approaches. Two widely used applications of statistical techniques in particle physics data include extracting ranges for parameters of interest (e.g., mass of the W boson, cross section for top production, neutrino mixing angles, etc.) and assessing the significance of possible signals (e.g., is there evidence for Higgs boson production?). These two topics are first discussed in the absence of systematics, and then methods of incorporating systematic effects are described. We give a detailed discussion of a Bayesian approach to setting upper limits on a Poisson process in the presence of background and/or acceptance uncertainties. The relevance of the choice of priors and how this affects the coverage properties of the method are described.