Ebook: Probability and Statistics in Experimental Physics

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.

---

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.

---

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.
Content:
Front Matter....Pages i-xi
Basic Probability Concepts....Pages 1-4
Some Initial Definitions....Pages 5-14
Some Results Independent of Specific Distributions....Pages 15-28
Discrete Distributions and Combinatorials....Pages 29-34
Specific Discrete Distributions....Pages 35-43
The Normal (or Gaussian) Distribution and Other Continuous Distributions....Pages 44-57
Generating Functions and Characteristic Functions....Pages 58-65
The Monte Carlo Method: Computer Simulation of Experiments....Pages 66-80
Queueing Theory and Other Probability Questions....Pages 81-91
Two-Dimensional and Multidimensional Distributions....Pages 92-106
The Central Limit Theorem....Pages 107-118
Inverse Probability; Confidence Limits....Pages 119-145
Methods for Estimating Parameters. Least Squares and Maximum Likelihood....Pages 146-169
Curve Fitting....Pages 170-200
Bartlett S Function; Estimating Likelihood Ratios Needed for an Experiment....Pages 201-212
Interpolating Functions and Unfolding Problems....Pages 213-220
Fitting Data with Correlations and Constraints....Pages 221-230
Beyond Maximum Likelihood and Least Squares; Robust Methods....Pages 231-241
Back Matter....Pages 243-252

---

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.
Content:
Front Matter....Pages i-xi
Basic Probability Concepts....Pages 1-4
Some Initial Definitions....Pages 5-14
Some Results Independent of Specific Distributions....Pages 15-28
Discrete Distributions and Combinatorials....Pages 29-34
Specific Discrete Distributions....Pages 35-43
The Normal (or Gaussian) Distribution and Other Continuous Distributions....Pages 44-57
Generating Functions and Characteristic Functions....Pages 58-65
The Monte Carlo Method: Computer Simulation of Experiments....Pages 66-80
Queueing Theory and Other Probability Questions....Pages 81-91
Two-Dimensional and Multidimensional Distributions....Pages 92-106
The Central Limit Theorem....Pages 107-118
Inverse Probability; Confidence Limits....Pages 119-145
Methods for Estimating Parameters. Least Squares and Maximum Likelihood....Pages 146-169
Curve Fitting....Pages 170-200
Bartlett S Function; Estimating Likelihood Ratios Needed for an Experiment....Pages 201-212
Interpolating Functions and Unfolding Problems....Pages 213-220
Fitting Data with Correlations and Constraints....Pages 221-230
Beyond Maximum Likelihood and Least Squares; Robust Methods....Pages 231-241
Back Matter....Pages 243-252
....