Content. - 1: Probability Models. - 1. 1 Background. - 1. 2 Exchangeability. - 1. 4 DeFinetti's Representation Theorem. - 1. 5 Proofs of DeFinetti's Theorem and Related Results*. - 1. 6 Infinite-Dimensional Parameters*. - 1. 7 Problems. - 2: Sufficient Statistics. - 2. 1 Definitions. - 2. 2 Exponential Families of Distributions. - 2. 4 Extremal Families*. - 2. 5 Problems. - Chapte 3: Decision Theory. - 3. 1 Decision Problems. - 3. 2 Classical Decision Theory. - 3. 3 Axiomatic Derivation of Decision Theory*. - 3. 4 Problems. - 4: Hypothesis Testing. - 4. 1 Introduction. - 4. 2 Bayesian Solutions. - 4. 3 Most Powerful Tests. - 4. 4 Unbiased Tests. - 4. 5 Nuisance Parameters. - 4. 6 P-Values. - 4. 7 Problems. - 5: Estimation. - 5. 1 Point Estimation. - 5. 2 Set Estimation. - 5. 3 The Bootstrap*. - 5. 4 Problems. - 6: Equivariance*. - 6. 1 Common Examples. - 6. 2 Equivariant Decision Theory. - 6. 3 Testing and Confidence Intervals*. - 6. 4 Problems. - 7: Large Sample Theory. - 7. 1 Convergence Concepts. - 7. 2 Sample Quantiles. - 7. 3 Large Sample Estimation. - 7. 4 Large Sample Properties of Posterior Distributions. - 7. 5 Large Sample Tests. - 7. 6 Problems. - 8: Hierarchical Models. - 8. 1 Introduction. - 8. 3 Nonnormal Models*. - 8. 4 Empirical Bayes Analysis*. - 8. 5 Successive Substitution Sampling. - 8. 6 Mixtures of Models. - 8. 7 Problems. - 9: Sequential Analysis. - 9. 1 Sequential Decision Problems. - 9. 2 The Sequential Probability Ratio Test. - 9. 3 Interval Estimation*. - 9. 4 The Relevancc of Stopping Rules. - 9. 5 Problems. - Appendix A: Measure and Integration Theory. - A. 1 Overview. - A. 1. 1 Definitions. - A. 1. 2 Measurable Functions. - A. 1. 3 Integration. - A. 1. 4 Absolute Continuity. - A. 2 Measures. - A. 3 Measurable Functions. - A. 4 Integration. - A. 5 Product Spaces. - A. 6 Absolute Continuity. - A. 7 Problems. - Appendix B: Probability Theory. - B. 1 Overview. - B. 1. 1Mathematical Probability. - B. 1. 2 Conditioning. - B. 1. 3 Limit Theorems. - B. 2 Mathematical Probability. - B. 2. 1 Random Quantities and Distributions. - B. 2. 2 Some Useful Inequalities. - B. 3 Conditioning. - B. 3. 1 Conditional Expectations. - B. 3. 2 Borel Spaces*. - B. 3. 3 Conditional Densities. - B. 3. 4 Conditional Independence. - B. 3. 5 The Law of Total Probability. - B. 4 Limit Theorems. - B. 4. 1 Convergence in Distribution and in Probability. - B. 4. 2 Characteristic Functions. - B. 5 Stochastic Processes. - B. 5. 1 Introduction. - B. 5. 3 Markov Chains*. - B. 5. 4 General Stochastic Processes. - B. 6 Subjective Probability. - B. 7 Simulation*. - B. 8 Problems. - Appendix C: Mathematical Theorems Not Proven Here. - C. 1 Real Analysis. - C. 2 Complex Analysis. - C. 3 Functional Analysis. - Appendix D: Summary of Distributions. - D. 1 Univariate Continuous Distributions. - D. 2 Univariate Discrete Distributions. - D. 3 Multivariate Distributions. - References. - Notation and Abbreviation Index. - Name Index. Language: English