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Practical Statistics for Physicists

Louis Lyons Imperial College and Oxford CMS expt at LHC l.lyons@physics.ox.ac.uk. Practical Statistics for Physicists. CERN Latin American School March 2015. Extra Lecture: Learning to love the Error Matrix. Introduction via 2-D Gaussian Understanding covariance

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Practical Statistics for Physicists

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  1. Louis Lyons Imperial College and Oxford CMS expt at LHC l.lyons@physics.ox.ac.uk Practical Statistics for Physicists CERN Latin American School March 2015

  2. Extra Lecture:Learning to love the Error Matrix • Introduction via 2-D Gaussian • Understanding covariance • Using the error matrix Combining correlated measurements • Estimating the error matrix

  3. y = 1 exp{-(x-µ)2/(22)} 2  Reminder of 1-D Gaussian or Normal

  4. Correlations Basic issue: For 1 parameter, quote value and error For 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

  5. Element Eij - <(xi – xi) (xj – xj)> Diagonal Eij = variances Off-diagonal Eij = covariances

  6. Towards the Error Matrix

  7. Example from Particle Physics

  8. Examples of correlated variables

  9. Small error Example: Chi-sq Lecture xbest outside x1 x2 ybest outside y1  y2

  10. b y a x

  11. Conclusion Error matrix formalism makes life easy when correlations are relevant

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