Probability and Statistics in Experimental Physics

Byron P. Roe (Autor)

Buch | Hardcover

252 Seiten

2001 | 2nd ed. 2001
Springer-Verlag New York Inc.
978-0-387-95163-8 (ISBN)

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Intended for advanced undergraduates and graduate students, this book is a practical guide to the use of probability and statistics in experimental physics. The emphasis is on applications and understanding, on theorems and techniques actually used in research. The text is not a comprehensive text in probability and statistics; proofs are sometimes omitted if they do not contribute to intuition in understanding the theorem. The problems, some with worked solutions, introduce the student to the use of computers; occasional reference is made to routines available in the CERN library, but other systems, such as Maple, can also be used. Topics covered include: basic concepts; definitions; some simple results independent of specific distributions; discrete distributions; the normal and other continuous distributions; generating and characteristic functions; the Monte Carlo method and computer simulations; multi-dimensional distributions; the central limit theorem; inverse probability and confidence belts; estimation methods; curve fitting and likelihood ratios; interpolating functions; fitting data with constraints; robust estimation methods. This second edition introduces a new method for dealing with small samples, such as may arise in search experiments, when the data are of low probability. It also includes a new chapter on queuing problems (including a simple, but useful buffer length example). In addition new sections discuss over- and under-coverage using confidence belts, the extended maximum-likelihood method, the use of confidence belts for discrete distributions, estimation of correlation coefficients, and the effective variance method for fitting y = f(x) when both x and y have measurement errors.

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.

Reihe/Serie	Undergraduate Texts in Contemporary Physics
Zusatzinfo	XII, 252 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	156 x 234 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Statistik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
ISBN-10	0-387-95163-6 / 0387951636
ISBN-13	978-0-387-95163-8 / 9780387951638
Zustand	Neuware