Probability, statistics, and associated computing techniques

This chapter attempts to explore the extent to which it is possible for the experimental physicist to find optimal statistical techniques to provide a unique and unambiguous quantitative measure of the significance of raw data. Discusses statistics as the inverse of probability; normal theory of parameter estimation; normal theory (Gaussian measurements); the universality of the Gaussian distribution; real-life resolution functions; combination and propagation of uncertainties; the sum or difference of 2 variables; local theory, or the propagation of small errors; error on the ratio of 2 discrete variables; the propagation of large errors; confidence intervals; classical theory; Bayesian theory; use of the likelihood function; the second derivative of the log-likelihood function; multiparameter confidence intervals; the method of MINOS; least squares; the Gauss-Markov theorem; maximum likelihood for uniform error distribution; the Chebyshev fit; the parameter uncertainties; the efficiency of the Chebyshev estimator; error symmetrization; robustness vs. efficiency; testing of hypotheses (e.g., the Neyman-Pearson test); goodness-of-fit; distribution-free tests; comparing two one-dimensional distributions; comparing multidimensional distributions; and permutation tests for comparing two point sets