Probability and Statistics for Physical Sciences

2nd Edition - September 5, 2023
Authors: Brian Martin, Mark Hurwitz
Language: English
Paperback ISBN:
9 7 8 - 0 - 4 4 3 - 1 8 9 6 9 - 2
eBook ISBN:
9 7 8 - 0 - 4 4 3 - 1 8 9 7 0 - 8

Probability and Statistics for Physical Sciences, Second Edition is an accessible guide to commonly used concepts and methods in statistical analysis used in the physical scienc… Read more

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Probability and Statistics for Physical Sciences, Second Edition is an accessible guide to commonly used concepts and methods in statistical analysis used in the physical sciences. This brief yet systematic introduction explains the origin of key techniques, providing mathematical background and useful formulas. The text does not assume any background in statistics and is appropriate for a wide-variety of readers, from first-year undergraduate students to working scientists across many disciplines.

Cover image
Title page
Table of Contents
Copyright
Preface
Acknowledgments
CHAPTER 1. Statistics, experiments, and data
1.1 Experiments and observations
1.2 Random variables and sampling
1.3 Displaying data
1.4 Summarizing data numerically
1.5 Large samples
1.6 Experimental errors
Problems 1
CHAPTER 2. Probability
2.1. Sample spaces and events
2.2. Axioms and calculus of probability
2.3. Conditional and marginal probabilities
2.4. Permutations and combinations
2.5. The meaning of probability
Problems 2
CHAPTER 3. Probability distributions I: Basic concepts
3.1. Random variables
3.2. Single variable
3.3. Several variables
3.4. Functions of a random variable
Problems 3
CHAPTER 4. Probability distributions II: Examples
4.1 Continuous variables
4.2 Discrete variables
Problems 4
CHAPTER 5. Sampling and estimation
5.1. Random samples and estimators
5.2. Estimators for the mean, variance, and covariance
5.3. Laws of large numbers and the central limit theorem
5.4. Experimental errors
5.5. Monte Carlo method and simulations
Problems 5
CHAPTER 6. Sampling distributions associated with the normal distribution
6.1. Chi-squared distribution
6.2. Student’s t distribution
6.3. F distribution
6.4. Relations between χ2, t, and F distributions
Problems 6
Chapter 7. Parameter estimation I: Maximum likelihood and minimum variance
7.1. Estimation of a single parameter
7.2. Variance of an estimator
7.3. Simultaneous estimation of several parameters
7.4. Minimum variance
Problems 7
CHAPTER 8. Parameter estimation II: Least-squares and other methods
8.1. Unconstrained linear least-squares
8.2. Linear least-squares with constraints
8.3. Nonlinear least-squares
8.4. Other methods
Problems 8
CHAPTER 9. Interval estimation
9.1 Confidence intervals: Basic ideas
9.2 Confidence intervals: General method
9.3 Normal distribution
9.4 Poisson distribution
9.5 Large samples
9.6 Confidence intervals near boundaries
9.7 Bayesian confidence intervals
Problems 9
CHAPTER 10. Hypothesis testing I: Parameters
10.1. Statistical hypotheses
10.2. General hypotheses: Likelihood ratios
10.3. Normal distribution
10.4. Other distributions
10.5. Analysis of variance
10.6. Bayesian hypothesis testing
Problems 10
CHAPTER 11. Hypothesis testing II: Other tests
11.1 Goodness-of-fit tests
11.2 Tests for independence
11.3 Nonparametric tests
Problems 11
Appendix A. Miscellaneous mathematics
Appendix B. Optimization of nonlinear functions
Appendix C. Statistical tables
Appendix D. Answers to selected problems
Bibliography
Index