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Data Analysis in High Energy Physics : a Practical Guide to Statistical Methods.
This practical guide covers the essential tasks in statistical data analysis encountered in high energy physics and provides comprehensive advice for typical questions and problems. The basic methods for inferring results from data are presented as well as tools for advanced tasks such as improving...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Wiley,
2013.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Data Analysis in High Energy Physics; Contents; Preface; List of Contributors; 1 Fundamental Concepts; 1.1 Introduction; 1.2 Probability Density Functions; 1.2.1 Expectation Values; 1.2.2 Moments; 1.2.3 Associated Functions; 1.3 Theoretical Distributions; 1.3.1 The Gaussian Distribution; 1.3.2 The Poisson Distribution; 1.3.3 The Binomial Distribution; 1.3.4 Other Distributions; 1.4 Probability; 1.4.1 Mathematical Definition of Probability; 1.4.2 Classical Definition of Probability; 1.4.3 Frequentist Definition of Probability; 1.4.4 Bayesian Definition of Probability.
- 1.5 Inference and Measurement1.5.1 Likelihood; 1.5.2 Frequentist Inference; 1.5.3 Bayesian Inference; 1.6 Exercises; References; 2 Parameter Estimation; 2.1 Parameter Estimation in High Energy Physics: Introductory Words; 2.2 Parameter Estimation: Definition and Properties; 2.3 The Method of Maximum Likelihood; 2.3.1 Maximum-Likelihood Solution; 2.3.2 Properties of the Maximum-Likelihood Estimator; 2.3.3 Maximum Likelihood and Bayesian Statistics; 2.3.4 Variance of the Maximum-Likelihood Estimator; 2.3.5 Minimum-Variance Bound and Experiment Design; 2.4 The Method of Least Squares.
- 2.4.1 Linear Least-Squares Method2.4.2 Non-linear Least-Squares Fits; 2.5 Maximum-Likelihood Fits:Unbinned, Binned, Standard and Extended Likelihood; 2.5.1 Unbinned Maximum-Likelihood Fits; 2.5.2 Extended Maximum Likelihood; 2.5.3 Binned Maximum-Likelihood Fits; 2.5.4 Least-Squares Fit to a Histogram; 2.5.5 Special Topic: Averaging Data with Inconsistencies; 2.6 Bayesian Parameter Estimation; 2.7 Exercises; References; 3 Hypothesis Testing; 3.1 Basic Concepts; 3.1.1 Statistical Hypotheses; 3.1.2 Test Statistic; 3.1.3 Critical Region; 3.1.4 Type I and Type II Errors.
- 3.1.5 Summary: the Testing Process3.2 Choosing the Test Statistic; 3.3 Choice of the Critical Region; 3.4 Determining Test Statistic Distributions; 3.5 p-Values; 3.5.1 Significance Levels; 3.5.2 Inclusion of Systematic Uncertainties; 3.5.3 Combining Tests; 3.5.4 Look-Elsewhere Effect; 3.6 Inversion of Hypothesis Tests; 3.7 Bayesian Approach to Hypothesis Testing; 3.8 Goodness-of-Fit Tests; 3.8.1 Pearson's 2 Test; 3.8.2 Run Test; 3.8.3 2 Test with Unbinned Measurements; 3.8.4 Test Using the Maximum-Likelihood Estimate; 3.8.5 Kolmogorov-Smirnov Test; 3.8.6 Smirnov-Cramér-von Mises Test.
- 3.8.7 Two-Sample Tests3.9 Conclusion; 3.10 Exercises; References; 4 Interval Estimation; 4.1 Introduction; 4.2 Characterisation of Interval Constructions; 4.3 Frequentist Methods; 4.3.1 Neyman's Construction; 4.3.2 Test Inversion; 4.3.3 Pivoting; 4.3.4 Asymptotic Approximations; 4.3.5 Bootstrapping; 4.3.6 Nuisance Parameters; 4.4 Bayesian Methods; 4.4.1 Binomial Efficiencies; 4.4.2 Poisson Means; 4.5 Graphical Comparison of Interval Constructions; 4.6 The Role of Intervals in Search Procedures; 4.6.1 Coverage; 4.6.2 Sensitivity; 4.7 Final Remarks and Recommendations; 4.8 Exercises; References.