Practical statistics for particle physics

✍ Scribed by Barlow R.J.

• Year: 2022
• Tongue: English
• Leaves: 49
• Category: Library

✦ Table of Contents

1 Introduction
2 Probability
2.1 What is probability?
2.2 Mathematical probability
2.3 Real probability
2.4 Frequentist probability
2.5 Bayes' theorem
2.6 Bayesian probability
2.7 Summary
3 Probability distributions and their properties
3.1 Expectation values
3.2 Binomial, Poisson and Gaussian
4 Hypothesis testing
4.1 Type I and type II errors
4.2 The Neymann-Pearson lemma
4.3 Efficiency, purity, and ROC plots
4.4 The null hypothesis
5 Estimation
5.1 Bias
5.2 Efficiency
5.3 Maximum likelihood estimation
5.4 Least squares
5.5 Straight line fits
5.6 Fitting histograms
6 Errors
6.1 Errors from likelihood
6.2 Combining errors
6.3 Asymmetric errors
6.4 Errors in 2 or more dimensions
6.5 Systematic errors
7 Goodness of fit
7.1 The chi distribution
7.2 Wilks' theorem
7.3 Toy Monte Carlos and likelihood for goodness of fit
8 Upper limits
8.1 Frequentist confidence
8.2 Confidence belts
8.3 Coverage
8.4 Upper limits
8.5 Bayesian `credible intervals'
8.6 Limits in the presence of background
9 Making a discovery
9.1 Sigma language
9.2 The look-elsewhere effect
9.3 Blind analysis
10 Conclusions