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Statistics and Data Analysis (HEP)

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The Gaussian Limit

The central limit theorem,

Gaussian errors,

Error propagation,

Combination of measurements,

Multidimensional Gaussian errors,

Error Matrix

Statistics and Data Analysis (HEP)

Prof. dr hab. Elżbieta Richter-Wąs

Follow the course/slides from M. A. Thomson lectures at Cambridge University

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How to calculate uncertainties?

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The Central Limit Theorem

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A useful integral relationship

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Properties of Gaussian Distribution

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Properties of the 1D Gaussian Distribution, cont.

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Averaging Gaussian Measurements

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Averaging Gaussian Measurements II

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Error Propagation I

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Error on Error

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(see Appendix)

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Combining Gaussian Errors

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Correlated errors: covariance

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Error propagation II: the general case

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Example continued

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Estimating the Correlation Coefficient

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Properties of the 2D Gaussian Distribution

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Properties of 2D Gaussian Distribution

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The Error Ellipse and Error Matrix

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General transformation of Errors

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A simple example

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A more involved example

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Summary

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Appendix: Error on Error - Justification

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Cytaty

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