Optimal statistical decisions [[electronic resource] /] / Morris H. DeGroot

• Record Nr.: UNINA9910830263903321
• Autore: DeGroot Morris H. <1931-1989.>
• Pubbl/distr/stampa: Hoboken, N.J., : Wiley-Interscience, 2004
• ISBN: 1-280-27340-2; 9786610273409; 0-470-32377-9; 0-471-72614-1; 0-471-72900-0
• Edizione: [Wiley classics library ed.]
• Descrizione fisica: 1 online resource (511 p.)
• Collana: Wiley classics library
• Disciplina: 519.8
• Soggetti: Statistical decision; Bayesian statistical decision theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 447-471) and indexes.
• Nota di contenuto: optimal statistical decisions; Foreword; Preface; contents; part one: survey of probability theory; Chapter 1. INTRODUCTION; Chapter 2. EXPERIMENTS, SAMPLE SPACES, AND PROBABILITY; 2.1 Experiments and Sample Spaces; 2.2 Set Theory; 2.3 Events and Probability; 2.4 Conditional Probability; 2.5 Binomial Coefficients; Exercises; Chapter 3. RANDOM VARIABLES, RANDOM VECTORS, AND DISTRIBUTION FUNCTIONS; 3.1 Random Variables and Their Distributions; 3.2 Multivariate Distributions; 3.3 Sums and Integrals; 3.4 Marginal Distributions and Independence; 3.5 Vectors and Matrices; 3.6 Expectations, Moments, and Characteristic Functions3.7 Transformations of Random Variables; 3.8 Conditional Distributions; Exercises; Chapter 4. SOME SPECIAL UNlVARIATE DISTRIBUTIONS; 4.1 Introduction; 4.2 The Bernoulli Distribution; 4.3 The Binomial Distribution; 4.4 The Poisson Distribution; 4.5 The Negative Binomial Distribution; 4.6 The Hypergeometric Distribution; 4.7 The Normal Distribution; 4.8 The Gamma Distribution; 4.9 The Beta Distribution; 4.10 The Uniform Distribution; 4.11 The Pareto Distribution; 4.12 The t Distribution; 4.13 The F Distribution; Exercises; Chapter 5. SOME SPECIAL MULTIVARIATE DISTRIBUTIONS5.1 Introduction; 5.2 The Multinomial Distribution; 5.3 The Dirichlet Distribution; 5.4 The Multivariate Normal Distribution; 5.5 The Wishart Distribution; 5.6 The Multivariate t Distribution; 5.7 The Bilateral Bivariate Pareto Distribution; Exercises; part two: subjective probability and utility; Chapter 6. SUBJECTIVE PROBABILITY; 6.1 Introduction; 6.2 Relative Likelihood; 6.3 The Auxiliary Experiment; 6.4 Construction of the Probability Distribution; 6.5 Verification of the Properties of a Probability Distribution; 6.6 Conditional LikelihoodsExercises; Chapter 7. UTILITY; 7.1 Preferences among Rewards; 7.2 Preferences among Probability Distributions; 7.3 The Definition of a Utility Function; 7.4 Some Properties of Utility Functions; 7.5 The Utility of Monetary Rewards; 7.6 Convex and Concave Utility Functions; 7.7 The Axiomatic Development of Utility; 7.8 Construction of the Utility Function; 7.9 Verification of the Properties of a Utility Function; 7.10 Extension of the Properties of a Utility Function to the Class PE; Exercises; part three: statistical decision problems; Chapter 8. DECISION PROBLEMS; 8.1 Elements of a Decision Problem8.2 Bayes Risk and Bayes Decisions; 8.3 Nonnegative Loss Functions; 8.4 Concavity of the Bayes Risk; 8.5 Randomization and Mixed Decisions; 8.6 Conve Sets; 8.7 Decision Problems in Which ~ 2 and D Are Finite; 8.8 Decision Problems with Observations; 8.9 Construction of Bayes Decision Functions; 8.10 The Cost of Observation; 8.11 Statistical Decision Problems in Which Both O and D Contain Two Points; 8.12 Computation of the Posterior Distribution When the Observations Are Made in More Than One Stage; Exercises; Chapter 9. CONJUGATE PRIOR DISTRIBUTIONS; 9.1 Sufficient Statistics
• Sommario/riassunto: The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.