Probability and Statistics in Experimental Physics

Eine Einführung in die Wahrscheinlichkeitsrechnung und Statistik, wie sie in der Experimentalphysik benötigt wird. Der Autor legt den Schwerpunkt auf Anwendung und Verständnis, ohne die mathematische Genauigkeit zu vernachlässigen.

This book is intended as a practical guide for advanced undergraduates to the use of probability and statistics in experimental physics. The emphasis is on applications and understanding, on techniques that are used in experimental physics, and on the use of computers. This second edition includes a new chapter on queuing problems (such as, how large a buffer does one need deal with a random stream of data), and it introduces a new method for dealing with experiments in which only a few events are observed.

From the reviews of the second edition:

"This book is the second edition of a practical introduction into probability and statistics in experimental physics. The book is primarily written for undergraduate and graduate students and contains a new chapter on queueing theory and an additional discussion of the Feldman-Cousins unified method for estimating confidence intervals." (Ulrich Horst, Zentralblatt MATH, Vol. 1011, 2003)

"The book under review is rather unconventional in many respects, in particular concerning the choice of covered topics and the style of presentation. Its main goal is to provide the reader with techniques actually used in experimental research. They are illustrated by a series of worked problems. some material is included that one hardly finds in other books of this kind, like elements of queuing theory . many experimental physicists would appreciate probably to have a copy of this book within hand-reach." (F. Binon, Physicalia, Vol. 38 (5), 2002)

Inhalt

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.- 11.1Introduction; 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 Gibb's 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 Function; 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. InterpolatingFunctions 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.