2006-2007 ACADEMIC TRAINING PROGRAMME
LECTURE SERIES
9, 10, 11, 12, 13 October
from 11:00 to 12:00 - Main Auditorium, bldg. 500, TH Auditorium, bldg 4, 3rd floor, on 13 October

Practical Statistics for Particle Physicists
L. LYONS, University of Oxford, GB

Lecture 1: Learning to love the errror matrix Introductory remarks. Conditional probability. Statistical and systematic errors. Combining results Binomial, Poisson and 1-D Gaussian 2-D Gaussian and the error matrix. Understanding the covariance. Using the error matrix. Estimating the error matrix. Combining correlated measurements

Lecture 2: Parameter determination by likelihood: Do's and don'ts Introduction to likelihood. Error estimate. Simple examples: (1) Breit Wigner (2) Lifetime binned and unbinned likelihood several parameters extended maximum likelihood.
Common misapprehensions:
Normalisation
delta(lnL) = 1/2 rule and coverage
Integrating the likelihood
Unbinned L_max as goodness of fit
Punzi effect

Lecture 3: Chi-squared and hypothesis testing Basic idea. Error estimates. Several parameters correlated errors on y. Errors on x and y. Goodness of fit. Degrees of freedom. Why assymptotic? Errors of first kind and second kind.THE paradox Kinematic fits. Toy example.

Lecture 4: Bayes, Frequentism and limits Bayes and frequentist probability. Everyday examples. Prob(data;theory) is not equal to Prob(theory;data) Bayes theorem. Bayesian prior. When priors are and are not important. Frequentist confidence intervals, and their properties. Limits calculations by Bayes, Neyman construction and Feldman-Cousins Summary of Bayes and Frequentist approaches

Lecture 5: Discovery and p-values. Distinguishing a peak, a goof, and a statistical fluctuation Why 5 sigma for discovery? Blind analyses. What p-values are and what they are not. Combining p-values. Simultaneous optimisation for discovery and exclusion Incorporating systematic effects.