1 χ 2 and Goodness of Fit Louis Lyons IC and Oxford SLAC Lecture 2’, Sept 2008.
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Practical Statistics for Particle Physicists
CERN Academic Lectures
October 2006
Louis Lyons
Oxford
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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