Statistical Methods In Experimental Physics (2nd Edition) / Edition 2

The first edition of this classic book has become the authoritative reference for physicists desiring to master the finer points of statistical data analysis. This second edition contains all the important material of the first, much of it unavailable from any other sources. In addition, many chapters have been updated with considerable new material, especially in areas concerning the theory and practice of confidence intervals, including the important Feldman-Cousins method. Both frequentist and Bayesian methodologies are presented, with a strong emphasis on techniques useful to physicists and other scientists in the interpretation of experimental data and comparison with scientific theories. This is a valuable textbook for advanced graduate students in the physical sciences as well as a reference for active researchers

Table Of Contents:

Preface to the Second Edition v
Preface to the First Edition vii
Introduction 1
Outline 1
Language 2
Two Philosophies 3
Notation 4
Basic Concepts in Probability 9
Definitions of Probability 9
Mathematical probability 10
Frequentist probability 10
Bayesian probability 11
Properties of Probability 12
Addition law for sets of elementary events 12
Conditional probability and independence 13
Example of the addition law: scanning efficiency 14
Bayes theorem for discrete events 15
Bayesian use of Bayes theorem 16
Random variable 17
Continuous Random Variables 18
Probability density function 19
Change of variable 20
Cumulative, marginal and conditional distributions 21
Bayes theorem for continuous variables 22
Bayesian use of Bayes theorem for continuous variables 22
Properties of Distributions 24
Expectation, mean and variance 24
Covariance andcorrelation 26
Linear functions of random variables 28
Ratio of random variables 30
Approximate variance formulae 32
Moments 33
Characteristic Function 34
Definition and properties 34
Cumulants 37
Probability generating function 38
Sums of a random number of random variables 39
Invariant measures 41
Convergence and the Law of Large Numbers 43
The Tchebycheff Theorem and Its Corollary 43
Tchebycheff theorem 43
Bienayme-Tchebycheff inequality 44
Convergence 45
Convergence in distribution 45
The Paul Levy theorem 46
Convergence in probability 46
Stronger types of convergence 47
The Law of Large Numbers 47
Monte Carlo integration 48
The Central Limit theorem 49
Example: Gaussian (Normal) random number generator 51
Probability Distributions 53
Discrete Distributions 53
Binomial distribution 53
Multinomial distribution 56
Poisson distribution 57
Compound Poisson distribution 60
Geometric distribution 62
Negative binomial distribution 63
Continuous Distributions 64
Normal one-dimensional (univariate Gaussian) 64
Normal many-dimensional (multivariate Gaussian) 67
Chi-square distribution 70
Students t-distribution 73
Fisher-Snedecor F and Z distributions 77
Uniform distribution 79
Triangular distribution 79
Beta distribution 80
Exponential distribution 82
Gamma distribution 83
Cauchy, or Breit-Wigner, distribution 84
Log-Normal distribution 85
Extreme value distribution 87
Weibull distribution 89
Double exponential distribution 89
Asymptotic relationships between distributions 90
Handling of Real Life Distributions 91
General applicability of the Normal distribution 91
Johnson empirical distributions 92
Truncation 93
Experimental resolutions 94
Examples of variable experimental resolution 95
Information 99
Basic Concepts 100
Likelihood function 100
Statistic 100
Information of R.A. Fisher 101
Definition of information 101
Properties of information 101
Sufficient Statistics 103
Sufficiency 103
Examples 104
Minimal s