Description
Book SynopsisServing as a text for a two semester sequence on probability and statistical inference complex Models for Probability and Statistical Inference: Theory and Applications features exercises throughout the book and selected answers (not solutions). Each section is followed by a selection of problems, from simple to more complex.
Trade Review"The prose throughout the book is clear and well aimed at first-year master's student who is intelligent but not yet statistically sophisticated. Examples are clear and well chosen." (
Biometrics, March 2009)
"Highly recommended. Graduate students through professionals." (CHOICE, May 2008)
Table of Contents1. Probability Models. 1.1 Discrete Probability Models.
1.2 Conditional Probability and Independence.
1.3 Random Variables.
1.4 Expectation.
1.5 The Variance.
1.6 Covariance and Correlation.
2. Special Discrete Distributions.
2.1 The Binomial Distribution.
2.2 The Hypergeometric Distribution.
2.3 The Geometric and Negative Binomial Distributions.
2.4 The Poisson Distribution.
3. Continuous Random Variables.
4.1 Continuous RV's and Their Distributions.
4.2 Expected Values and Variances.
4.3 Transformations of Random Variables.
4.4Joint Densities.
4 Special Continuous Distributions.
4.1 The Normal Distribution.
4.2 The Gamma Distribution.
5. Conditional Distributions.
5.1 The Discrete Case.
5.2 Conditional Expectations for the Discrete Case.
5.3 Conditional Densities and Expectations for Continuous RV's.
6. Limit Laws.
6.1 Moment Generating Functions.
6.2 Convergence in Probability and in Distribution.
6.3 The Central Limit Theorem.
6.4 The Delta-Method.
7. Estimation.
7.1 Point Estimation.
7.2 The Method of Moments.
7.3 Maximum Likelihood.
7.4 Consistency.
7.5 The Ω-Method.
7.6 Confidence Intervals.
7.7 Fisher Information, The Cramer-Rao Bound, and Asymptotic Normality of MLE's.
7.8 Sufficiency.
8. Testing Hypotheses.
8.1 Introduction.
8.2 The Neyman-Pearson Lemma.
8.3 The Likelihood Ratio Test.
8.4 The p-Value and the Relationship Between Tests of Hypotheses and Confidence Intervals.
9. The Multivariate Normal, Chi-square, t, and F-Distributions.
9.1 The Multivariate Normal Distribution.
9.2 The Central and Noncentral Chi-Square Distributions.
9.3 Student's t-Distribution.
9.4 The F-Distribution.
10.3 Nonparametric Statistics.
10.1 The Wilcoxon Test and Estimator.
10.2 One Sample Methods.
10.3 The Kolmogorov-Smirnov Tests.
11. Linear Models.
11.1 The Principle of Least Squares.
11.2 Linear Models.
11.3 F-Tests for H0.
11.4 Two-Way Analysis of Variance..
12. Frequency Data.
12.1 Logistic Regression.
12.2 Two-Way Frequency Tables.
12.3 Chi-Square Goodness of Fit Tests.
13. Miscellaneous Topics.
13.1 Survival Analysis.
13.2 Bootstrapping.
13.3 Bayesian Statistics.
13.4 Sampling.
