Dear IPNS members, Lectures on Practical Statistics will be held as follows. Place: 4th building Room 414 Date: Thursday 10:30-12:00 ( starting October 30 ) Contents: As attached below. This lecture is given by Prof. Louis Lyons, who is now visiting KEK. He is a member of Delphi and CDF collaborations and known as the author of "Statistics for nuclear and particle physicists" (Cambridge University Press). The lectures are for students of the Graduate University for Advanced Studies, but is also useful for researchers, thus it is open to everybody. Your participation are highly welcomed. regards Akiya Miyamoto ============================================================================= Practical Statistics Lectures for Physicists -------------------------------------------- This course emphasises practical aspects of using Statistics to derive results from experimental data in an efficient manner. Many examples are used to illustrate the ideas. The first couple of lectures should be understandable by students with little experience of Statistics, and will probably be too elementary for post-docs and faculty. The later ones may be of interest to other members of the Institute as well. There will be plenty of opportunity for discussion. Problem sets will be distributed. I am due to stay at KEK till late January. I will be most happy to talk to anyone about statistical problems they may have. Just send me an e-mail (l.lyons@physics.ox.ac.uk), and we can arrange to meet. INTRODUCTION Why errors are important Random and systematic errors Probability and Statistics Estimating parameters Confidence ranges Goodness of fit Hypothesis testing Decisions Conditional probability Independence Mean, variance, and their accuracy Combining errors Linear Products and ratios Other (Analytic, numeric) Common sense Combining results Paradox 'Extra information is good for you' DISTRIBUTIONS Binomial Mean, variance Use for efficiency measurement Poisson Mean, variance When not valid Gaussian Interpretation of sigma Area in tail(s) Central Limit theorem Experimental resolution Student's t LEARNING TO LOVE THE ERROR MATRIX What it means Error matrix via 2-D Gaussian Introducing correlations Rotation of axes Straight line fitting Numerics Estimating error matrix elements Using the error matrix z=f(x,y) Change of variables General transformation Physics examples Combining results PARAMETER DETERMINATION (POINT ESTIMATES AND RANGES) Philosophy To normalise? Should parameter ranges be physical? Method of moments Maximum likelihood What it is How it works. Resonance Error estimates Example of lifetime determination What likelihood does not do. Unbinned and binned likelihoods Likelihood and goodness of fit Extended likelihood. Particle content of cosmic rays Least squares Introduction Error estimates Example of straight line fit Standard With correlations Errors on x and y Summary of different techniques GOODNESS OF FIT and HYPOTHESIS TESTING S and chi-squared Degrees of freedom Chi-squared distributions and tail areas. 'Impress your colleagues' What it is and what it is not The paradox Problems with sparse data. Other goodness of fit tests Likelihood ratio Errors of first and second kind Kinematic fitting What is it? Why do it? How do we do it? Toy example HEP examples BAYES and FREQUENTISM Definitions Probability Bayes Theorem For Frequentists For Bayesians Bayesian prior and posterior Examples from every-day life, and from Physics Tossing a coin Particle identification Hunter and dog Prob(data | theory) .ne. Prob(theory | data) Mistaken statements Unseen person Neyman construction Coverage Problems Importance of ordering rule Why Feldman and Cousins? Empty intervals Unified limits Flip-flop Simple examples (Gaussian, Poisson) Neutrino oscillations Summary table MONTE CARLO Integration examples Why do it? Non-uniform distributions Typical HEP examples Garden of Eden problem TOPICS FROM PARTICLE PHYSICS Maximisation BLUE technique Limits Estimates of significance Blind analyses Multivariate methods, especially neural networks etc