Probability and statistics in experimental physics

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