Statistics for Nuclear and Particle Physicists

Written by a non-statistician for non-statisticians, the book emphasizes the practical approach to those problems in statistics that arise regularly in data analysis situations in nuclear and high energy physics experiments. Rather than concentrate on proofs and theorems, the author provides an abundance of simple examples that illustrate the general ideas presented. This allows the reader to obtain maximum information in the simplest manner. Possible difficulties with the various techniques, and pitfalls to be avoided, are also discussed. This commonsense approach to statistical formalism enables nuclear physicists to better understand how to do justice to their analysis and interpretation of data.

Preface	p. xi
Experimental errors	p. 1
Why do we do experiments?	p. 1
Why estimate errors?	p. 1
Random and systematic errors	p. 3
The meaning of [sigma]	p. 7
Distributions	p. 7
Mean and variance	p. 9
Gaussian distribution	p. 13
Combining errors	p. 16
Linear situations	p. 16
Non-linear situations	p. 23
Combining results of different experiments	p. 25
Probability and statistics	p. 30
Probability	p. 30
Rules of probability	p. 32
Statistics	p. 35
Distributions	p. 39
Binomial	p. 39
Poisson	p. 41
Gaussian distribution	p. 47
Gaussian distribution in two variables	p. 53
Using the error matrix	p. 62
Specific examples of error matrix manipulations	p. 65
Parameter fitting and hypothesis testing	p. 74
Normalisation	p. 75
Interpretation of estimates	p. 77
Meaning of error estimates	p. 77
Upper limits	p. 78
Estimates outside the physical range	p. 80
The method of moments	p. 81
Maximum likelihood method	p. 85
What is it? Some simple examples	p. 85
The logarithm of the likelihood function, and error estimates	p. 88
Comments on the maximum likelihood method	p. 91
Several parameters	p. 96
Extended maximum likelihood method	p. 98
Least squares	p. 102
What is it?	p. 102
Notes on the least squares method	p. 106
Correlated errors for y[subscript i]	p. 109
Hypothesis testing	p. 111
Use of weighted sum of squared deviations	p. 111
Types of hypothesis testing	p. 115
Minimisation	p. 120
Detailed examples of fitting procedures	p. 125
Least squares fitting	p. 125
Function linear in parameters - the straight line	p. 125
General least squares case	p. 133
Straight line fit to points with errors on x and y	p. 137
Kinematic fitting	p. 142
General comments	p. 142
Actual fit in a simplified case	p. 144
Fit involving unmeasured variables	p. 147
Maximum likelihood determination of Breit-Wigner parameters	p. 152
Monte Carlo calculations	p. 161
Introduction	p. 161
What is it?	p. 161
Random numbers	p. 162
Why do Monte Carlo calculations?	p. 163
Accuracy of Monte Carlo calculations	p. 164
More than one dimension	p. 167
An integral by Monte Carlo methods	p. 168
Very simple applications of Monte Carlo calculations	p. 171
Evaluation of [pi]	p. 171
Mean transverse momentum	p. 172
Non-uniform distributions and correlated variables	p. 174
Typical uses of the Monte Carlo technique	p. 181
Designing experiments	p. 181
Testing programs	p. 183
Contamination estimates	p. 184
Geometrical correction factors	p. 185
Do theory and experiment agree?	p. 185
Resonance or statistical fluctuation?	p. 186
Phase space distributions	p. 189
Matrix elements	p. 190
Parameter determination	p. 190
Detailed examples	p. 191
Geometrical correction factors	p. 191
Physics	p. 197
Non-physics applications	p. 200
How to save yourself a fortune	p. 200
The Garden of Eden problem	p. 200
Background subtraction procedures	p. 204
The number of constraints in kinematic fitting	p. 211
Bibliography	p. 223
Index	p. 224
Table of Contents provided by Syndetics. All Rights Reserved.

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Statistics for Nuclear and Particle Physicists

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