1 Practical Statistics for Physicists Dresden March 2010 Louis Lyons Imperial College and Oxford CDF...
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1 Practical Statistics for Physicists Dresden March 2010 Louis Lyons Imperial College and Oxford CDF experiment at FNAL CMS expt at LHC [email protected]. uk
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Transcript of 1 Practical Statistics for Physicists Dresden March 2010 Louis Lyons Imperial College and Oxford CDF...
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Practical Statistics for Physicists
Dresden
March 2010
Louis Lyons
Imperial College and Oxford
CDF experiment at FNAL
CMS expt at LHC
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Topics
1) Learning to love the Error Matrix
2) Do’s and Dont’s with Likelihoods
3) Discovery and p-values
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Some of the questions to be addressedWhat is coverage, and do we really need it? Should we insist on at least a 5σ effect to claim
discovery?How should p-values be combined? If two different models both have respectable χ2
probabilities, can we reject one in favour of other?Are there different possibilities for quoting the
sensitivity of a search?How do upper limits change as the number of
observed events becomes smaller than the predicted background?
Combine 1 ± 10 and 3 ± 10 to obtain a result of 6 ± 1? What is the Punzi effect and how can it be
understood?
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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
CDF Statistics Committee
BaBar Statistics Working Group
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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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Gaussian or Normal
90.002
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Relevant for Goodness of Fit
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Correlations
Basic issue:For 1 parameter, quote value and errorFor 2 (or more) parameters, (e.g. gradient and intercept of straight line fit) quote values + errors + correlations
Just as the concept of variance for single variable is more general than Gaussian distribution, so correlation in more variables does not require multi-dim Gaussian
But more simple to introduce concept this way
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a
b
x
y
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Element Eij - <(xi – xi) (xj – xj)>
Diagonal Eij = variances
Off-diagonal Eij = covariances
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Small error
Example: Chi-sq Lecture
xbest outside x1 x2
ybest outside y1 y2
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a
b
x
y
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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
