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PRACTICAL STATISTICS FOR EXPERIMENTAL SCIENTISTS

Prof. L. Lyon, Oxford University

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These lectures are intended to be of practical help in explaining statistical ideas and techniques that are relevant for analyzing experimental data. The level is such that they should be readily accessible to graduate students who have had at least a little experience in analyzing experimental data, but especially from lecture 2 onwards, they should be of interest to post-docs as well. Some of the first lecture is a speedy reminder of topics which should be familiar from undergraduate courses.

Each lecture will last 2 hours including a break. There will be three lectures and one colloquium.

 

Synopsis of lectures


1) (a) INTRODUCTORY TOPICS and (b) LEARNING TO LOVE THE ERROR MATRIX
Sept. 13 15:00

(a) Probability and statistics. Conditional probability. Statistical and systematic errors. Combining errors. Combining results. Binomial, Poisson and 1-D Gaussian. 2-D Gaussian for uncorrelated variables.

(b) 2-D Gaussian and the error matrix. Understanding the covariance. Using the error matrix. Estimating the error matrix. Combining correlated measurements.


2) PARAMETER DETERMINATION BY LIKELIHOOD: DO's and DONT's
Sept. 14 10:00

Introduction to likelihood. Error estimate. Simple examples: (1) Peak mass and width (2) Lifetime. Binned and unbinned likelihood. Several parameters. Extended maximum likelihood. Common misconceptions: Normalization ∆(lnL) = 1⁄2 rule and coverage. Integrating the likelihood. Unbinned Lmax as goodness of fit? Punzi effect.

 

3) (a) LIMITS and (b) DISCOVERY ISSUES in SEARCH EXPERIMENTS
Sept 14 15:00

(a) Why limits? Different approaches. Comparison of numerical answers. Desirable properties of limits.

(b) CLAS discovery and un-discovery of penta-quarks. Distinguishing a peak and a statistical fluctuation. Goodness of fit, or hypothesis testing? Test statistic. Why 5 sigma for discovery?
Blind analyses. What p-values are and what they are not. p-values and likelihood ratios p0 versus p1 plots. Combining p-values. Bayesian methods. Simultaneous optimization for discovery and exclusion. Incorporating systematic effects.

 

4) COLLOQUIUM
BAYES VERSUS FREQUENTISM: AN ONGOING CONTROVERSY

Sept 15 10:00

These two very different approaches to analyzing data are described and contrasted, using examples both from every-day life and from the world of Physics. Their interpretations of 'probability' are contrasted. When used for determining parameters of a theory, cases where the resulting answers differ significantly are described. Finally, a summary is given of the differences between the Bayesian and Frequentist approaches.

 

LNGS - “B. PONTECORVO” ROOM


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