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Practical Statistics for Particle Physicists

CERN Academic Lectures

October 2006

Louis Lyons

Oxford

l.lyons@physics.ox.ac.uk

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Topics

1) Introduction

Learning to love the Error Matrix

2) Do’s and Dont’s with Likelihoods

3) χ2 and Goodness of Fit

4) Bayes, Frequentism and Limits

5) Discovery and p-values

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Books

Statistics for Nuclear and Particle Physicists Cambridge University Press, 1986

Available from CUP

Errata in these lectures

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Other Books

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Relevant for Goodness of Fit

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Gaussian = N(r, 0, 1)

Breit Wigner = 1/{π * (r2 + 1)}

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Learning to love the Error Matrix

• Introduction via 2-D Gaussian

• Understanding covariance

• Using the error matrix

Combining correlated measurements

• Estimating the error matrix

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Element Eij - <(xi – xi) (xj – xj)>

Diagonal Eij = variances

Off-diagonal Eij = covariances

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Small error

Example: Lecture 3

xbest outside x1 x2

ybest outside y1 y2

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Conclusion

Error matrix formalism makes life easy when correlations are relevant

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Next time: Likelihoods

• What it is

• How it works: Resonance

• Error estimates

• Detailed example: Lifetime

• Several Parameters

• Extended maximum L

• Do’s and Dont’s with L