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Ideas on Statistics Book Outline

This draft statistics book outline provides an introduction to the basics of statistics, explores statistical tests for event selection, discusses parameter estimation and interval estimation, addresses systematic uncertainties, and offers an overview of software tools and recommendations for statistical procedures.

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Ideas on Statistics Book Outline

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  1. Ideas on Statistics Book Outline ATLAS Statistics Forum CERN, 21 May, 2007 Glen Cowan Physics Department Royal Holloway, University of London g.cowan@rhul.ac.uk www.pp.rhul.ac.uk/~cowan Draft Statistics Book Outline

  2. ATLAS Statistics Book Outline (DRAFT) Introduction Overview of basics, probability, Bayesian vs. Frequentist issues, notation, terminology, pointers to resources Draft Statistics Book Outline

  3. Statistical tests for selecting events Optimizing selection: Neyman-Pearson, efficiency, purity, s/sqrt(s+b), etc. Multivariate methods Considerations concerning what variables to use, minimizing model uncertainty, validating with control samples, etc. Overview of important multivariate methods (linear discriminant, Neural Networks, SVM, decision trees). Draft Statistics Book Outline

  4. Statistical tests: establishing discovery General formalism of goodness-of-fit test: p-value of null hypothesis Including systematic uncertainties into a measure of significance Combining measurements Bayesian hypothesis tests, Bayes factors (?) Draft Statistics Book Outline

  5. Parameter estimation Likelihood function, properties of estimators (bias, variance) Overview of important fit methods: Maximum Likelihood, Least Squares. Variance of estimators: information inequality, etc. Goodness-of-fit in connection with parameter estimation Robustness, sensitivity of fit to model assumptions, Toy MC test of fit, etc. Simultaneous fits of several sets of measurements Including systematic uncertainties Draft Statistics Book Outline

  6. Interval estimation (setting limits) Interval from inversion of a test, confidence belt construction One-sided, two-sided, unified (Feldman-Cousins) intervals Properties of intervals and limits: coverage, mean (median) limit Multidimensional intervals, confidence regions Approximate confidence intervals from likelihood function Bayesian intervals Including systematic uncertainties Draft Statistics Book Outline

  7. Systematic uncertainties General considerations, types of systematic uncertainties Methods for dealing with nuisance parameters Bayesian methods for systematics Discussion of recipes for specific types of systematics, e.g., PDFs, jet energy scale, theoretical uncertainties, "n results from n essentially equivalent methods", etc. Quantifying correlations for systematic uncertainties Draft Statistics Book Outline

  8. Miscellaneous Overview of software tools Summary of recommendations for statistical procedures Draft Statistics Book Outline

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