Statistics for Physical Sciences is an informal, relatively short, but systematic, guide to the more commonly used ideas and techniques in statistical analysis, as used in physical sciences, together with explanations of their origins. It steers a path between the extremes of a recipe of methods with a collection of useful formulas, and a full mathematical account of statistics, while at the same time developing the subject in a logical way. The book can be read in its entirety by anyone with a basic exposure to mathematics at the level of a first-year undergraduate student of physical science and should be useful for practising physical scientists, plus undergraduate and postgraduate students in these fields.
Key Features
- Offers problems at the end of each chapter
- Features worked examples across all of the chapters
- Provides a collection of useful formulas in order to give a detailed account of mathematical statistics
Preface
Chapter 1. Statistics, Experiments, and Data
1.1. Experiments and Observations
1.2. Displaying Data
1.3. Summarizing Data Numerically
1.4. Large Samples
1.5. Experimental Errors
Chapter 2. Probability
2.1. Axioms of Probability
2.2. Calculus of Probabilities
2.3. The Meaning of Probability
Chapter 3. Probability Distributions I
3.1. Random Variables
3.2. Single Variates
3.3. Several Variates
3.4. Functions of a Random Variable
Chapter 4. Probability Distributions II
4.1. Uniform
4.2. Univariate Normal (Gaussian)
4.3. Multivariate Normal
4.4. Exponential
4.5. Cauchy
4.6. Binomial
4.7. Multinomial
4.8. Poisson
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
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 ?2, t, and F Distributions
Chapter 7. Parameter Estimation I
7.1. Estimation of a Single Parameter
7.2. Variance of an Estimator
7.3. Simultaneous Estimation of Several Parameters
7.4. Minimum Variance
Chapter 8. Parameter Estimation II
8.1. Unconstrained Linear Least Squares
8.2. Linear Least Squares with Constraints
8.3. Nonlinear Least Squares
8.4. Other Methods
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
Chapter 10. Hypothesis Testing I
10.1. Statistical Hypotheses
10.2. General Hypotheses: Likelihood Ratios
10.3. Normal Distribution
10.4. Other Distributions
10.5. Analysis of Variance
Chapter 11. Hypothesis Testing II
11.1. Goodness-of-Fit Tests
11.2. Tests for Independence
11.3. Nonparametric Tests
Appendix A. Miscellaneous Mathematics
Appendix B. Optimization of Nonlinear Functions
Appendix C. Statistical Tables
Appendix D. Answers to Odd-Numbered Problems
Bibliography
Index
Graduate and undergraduate students in the physical sciences. Physicists, astronomers, chemists, earth scientists and others.
