Probability and Statistics

This is the text chosen for Boston University's CAS MA 684, Multivariate Analysis, course, which I took in the spring semester of 2006. The course was an applied statistics course for statistics majors and graduate students in other fields who need to perform statistical analysis of their data.

The book provides a nice mix of theory and application. The chapters are short and concentrate on what main idea each. There is a lot of SAS output included in the book, but strangely the book doesn't include the SAS programs used to generate the output.

The book’s chapters are:

1. Concepts and examples of research
2. Classification of variables and the choice of analysis
3. Basic statistics: a review
4. Introduction to regression analysis
5. Straight-line regression analysis
6. The correlation coefficient and straight-line regression analysis
7. The analysis-of-variance table
8. Multiple regression analysis: general considerations
9. Testing hypotheses in multiple regression
10. Correlations: multiple, partial, and multiple partial
11. Confounding and interaction in regression
12. Regression diagnostics
13. Polynomial regression
14. Dummy variables in regression
15. Analysis of covariance and other methods for adjusting continuous data
16. Selecting the best regression equation
17. One-way analysis of variance
18. Randomized blocks: special case of two-way ANOVA
19. Two-way ANOVA with equal cell numbers
20. Two-way ANOVA with unequal cell numbers
21. Analysis of repeated measures data
22. The method of maximum likelihood
23. Logistic regression analysis
24. Poisson regression analysis

This is a beautifully produced book with 200 full color figures. It will take me years to master all the methods presented.

The book’s chapters are:

1. Introduction
2. Data manipulation
3. The S language
4. Graphics
5. Univariate statistics
6. Linear statistical models
7. Generalized linear models
8. Non-linear and smooth regression
9. Tree-based methods
10. Random and mixed effects
11. Exploratory multivariate analysis
12. Classification
13. Survival analysis
14. Time series analysis
15. Spatial statistics
16. Optimization

This is an excellent book on probability. Ross takes some interesting tangents to solve unusual problems.

The chapters are:

1. Combinatorial analysis
2. Axioms of probability
3. Conditional probability and independence
4. Random variables
5. Continuous random variables
6. Jointly distributed random variables
7. Properties of expectation
8. Limit theorems
9. Additional topics in probability
10. Simulation

This book was the required text for Boston University's MET MA 582, Mathematical Statistics, course.

This is a difficult book with enough material for three semesters. The material is well-written and rewards hard work. Most unusual, the book contains some S code that can be run using R or S-PLUS.

The chapters are:

1. Probability and distributions
2. Multivariate distributions
3. Some special distributions
4. Unbiasedness, consistency, and limiting distributions
5. Some elementary statistical inference
6. Maximum likelihood methods
7. Sufficiency
8. Optional tests of hypotheses
9. Inferences about normal models
10. Nonparametric statistics
11. Bayesian statistics
12. Linear models

A free PDF version of this book is now available.

The chapters are:

1. Discrete probability distributions
2. Continuous probability distributions
3. Combinatorics
4. Conditional probability
5. Distributions and densities
6. Expected value and variance
7. Sums of random variables
8. Law of large numbers
9. Central limits theorem
10. Generating functions
11. Markov chains
12. Random walks

When I was taking Mathematical Statistics at Boston University, sometimes the assigned text (Introduction to Mathematical Statistics by Hogg, McKean, and Craig) was too difficult. I purchased this book as a supplementary text and discovered that this book had probably provided the source material for the professor’s lectures.

This book covers the same material as Hogg, McKean, and Craig, but on a less rigorous level. There is less emphasis on theory and more emphasis on application.

The chapters are:

1. Introduction
2. Probability
3. Probability distributions and probability densities
4. Mathematical expectation
5. Special probability distributions
6. Special probability densities
7. Functions of random variables
8. Sampling distributions
9. Decision theory
10. Point estimation
11. Interval estimation
12. Hypothesis testing
13. Tests of hypothesis involving means, variances, and proportions
14. Regression and correlation
15. Design and analysis of experiments
16. Nonparametric tests

This statistics textbook is recommended for juniors, seniors, or graduate students who have had a year of introductory statistics, three semesters of calculus (through multivariate calculus), and a semester of linear algebra. I use this book regularly, and I recommend it highly.

The book includes a CD with mathStatica and a trial version of Mathematica 4.

Morrison provides an exceptionally clear presentation of multivariate statistics, including discriminant functions, covariance matrices, principal component analysis, and factor analysis. Linear algebra and matrices are used extensively throughout the book. This book is sadly out of print; I obtained my copy from an online used book dealer.

This book provides exhaustive coverage of principal component analysis, a popular method of reducing the dimensionality of multivariate data.

This book provides a series of in-depth case studies that present real-world data sets for analysis by the student. The book’s web site includes special intructions for users of R and S-PLUS.

A classic, this book is a highly readable introduction to experimental design. The 2nd edition was published in 2005.

This book presents probability and statistics for sequence analysis. A second edition has since been published.