Probability and statistics in experimental physics

Description

Cover Title page Preface 1. Basic Probability Concepts 2. Some Initial Definitions 2.1 Worked Problems 2.2 Exercises 3. Some Results Independent of Specific Distributions 3.1 Multiple Scattering and the Root N Law 3.2 Propagation of Errors; Errors When Changing Variables 3.3 Some Useful Inequalities 3.4 Worked Problems 3.5 Exercises 4. Discrete Distributions and Combinatorials 4.1 Worked Problems 4.2 Exercises 5. Specific Discrete Distributions 5.1 Binomial Distribution 5.2 Poisson Distribution 5.3 Worked Problems 5.4 Exercises 6. The Normal (or Gaussian) Distribution and Other Continuous Distributions 6.1 The Normal Distribution 6.2 The Chi-square Distribution 6.3 F Distribution 6.4 Student's Distribution 6.5 The Uniform Distribution 6.6 The Log-Normal Distribution 6.7 The Cauchy Distribution (Breit-Wigner Distribution) 6.8 Worked Problems 6.9 Exercises 7. Generating Functions and Characteristic Functions 7.1 Introduction 7.2 Convolutions and Compound Probability 7.3 Generating Functions 7.4 Characteristic Functions 7.5 Exercises 8. The Monte Carlo Method: Computer Simulation of Experiments 8.1 Using the Distribution Inverse 8.2 Method of Composition 8.3 Acceptance Rejection Method 8.4 Computer Pseudorandom Number Generators 8.5 Unusual Application of a Pseudorandom Number String 8.6 Worked Problems 8.7 Exercises 9. Queueing Theory and Other Probability Questions 9.1 Queueing Theory 9.2 Markov Chains 9.3 Games of Chance 9.4 Gambler's Ruin 9.5 Exercises 10. Two-Dimensional and Multidimensional Distributions 10.1 Introduction 10.2 Two-Dimensional Distributions 10.3 Multidimensional Distributions 10.4 Theorems on Sums of Squares 10.5 Exercises 11. The Central Limit Theorem 11.1 Introduction; Lindeberg Criterion 11.2 Failures of the Central Limit Theorem 11.3 Khintchine's Law of the Iterated Logarithm 11.4 Worked Problems 11.5 Exercises 12. Inverse Probability; Confidence Limits 12.1 Bayes' Theorem 12.2 The Problem of A Priori Probability 12.3 Confidence Intervals and Their Interpretation 12.4 Use of Confidence Intervals for Discrete Distributions 12.5 Improving on the Symmetric Tails Confidence Limits 12.6 When Is a Signal Significant? 12.7 Worked Problems 12.8 Exercises 13. Methods for Estimating Parameters. Least Squares and Maximum Likelihood 13.1 Method of Least Squares (Regression Analysis) 13.2 Maximum Likelihood Method 13.3 Further Considerations in Fitting Histograms 13.4 Improvement over Symmetric Tails Confidence Limits for Events With Partial Background-Signal Separation 13.5 Estimation of a Correlation Coefficient 13.6 Putting Together Several Probability Estimates 13.7 Worked Problems 13.8 Exercises 14. Curve Fitting 14.1 The Maximum Likelihood Method for Multiparameter Problems 14.2 Regression Analysis with Non-constant Variance 14.3 The Gibbs' Phenomenon 14.4 The Regularization Method 14.5 Other Regularization Schemes 14.6 Fitting Data With Errors in Both x and y 14.7 Non-linear Parameters 14.8 Optimizing a Data Set With Signal and Background 14.9 Robustness of Estimates 14.10 Worked Problems 14.11 Exercises 15. Bartlett S Fonction; Estimating Likelihood Ratios Needed for an Experiment 15.1 Introduction 15.2 The Jacknife 15.3 Making the Distribution Function of the Estimate Close to Normal; the Bartlett S Function 15.4 Likelihood Ratio 15.5 Estimating in Advance the Number of Events Needed for an Experiment 15.6 Exercises 16. Interpolating Functions and Unfolding Problems 16.1 Interpolating Functions 16.2 Spline Functions 16.3 B-Splines 16.4 Unfolding Data 16.5 Exercises 17. Fitting Data with Correlations and Constraints 17.1 Introduction 17.2 General Equations for Minimization 17.3 Iterations and Correlation Matrices 18. Beyond Maximum Likelihood and Least Squares; Robust Methods 18.1 Introduction 18.2 Tests on the Distribution Function 18.3 Tests Based on the Binomial Distribution 18.4 Tests Based on the Distributions of Deviations in Individual Bins of a Histogram 18.5 Exercises References Index