1 Practical Statistics for Particle Physicists CERN Academic Lectures October 2006 Louis Lyons Oxford

2 Topics 1) Introduction Learning to love the Error Matrix 2) Do’s and Dont’s with L ikelihoods 3) χ 2 and Goodness of Fit 4) Bayes, Frequentism and Limits 5) Discovery and p-values

3 Books Statistics for Nuclear and Particle Physicists Cambridge University Press, 1986 Available from CUP Errata in these lectures

4 Other Books

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12 Relevant for Goodness of Fit

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16 Gaussian = N(r, 0, 1) Breit Wigner = 1/{π * (r 2 + 1)}

17 Learning to love the Error Matrix Introduction via 2-D Gaussian Understanding covariance Using the error matrix Combining correlated measurements Estimating the error matrix

18 Element E ij - Diagonal E ij = variances Off-diagonal E ij = covariances

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30 Small error Example: Lecture 3 x best outside x 1  x 2 y best outside y 1  y 2

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34 Conclusion Error matrix formalism makes life easy when correlations are relevant

35 Next time: L ikelihoods What it is How it works: Resonance Error estimates Detailed example: Lifetime Several Parameters Extended maximum L Do’s and Dont’s with L