LEADER 05099nam 2200661 a 450 001 9910146070303321 005 20170815120138.0 010 $a1-280-27340-2 010 $a9786610273409 010 $a0-470-32377-9 010 $a0-471-72614-1 010 $a0-471-72900-0 035 $a(CKB)1000000000019155 035 $a(EBL)224947 035 $a(OCoLC)475932179 035 $a(SSID)ssj0000215746 035 $a(PQKBManifestationID)11184910 035 $a(PQKBTitleCode)TC0000215746 035 $a(PQKBWorkID)10194356 035 $a(PQKB)10586106 035 $a(MiAaPQ)EBC224947 035 $a(EXLCZ)991000000000019155 100 $a20040521d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOptimal statistical decisions$b[electronic resource] /$fMorris H. DeGroot 205 $aWiley classics library ed. 210 $aHoboken, N.J. $cWiley-Interscience$d2004 215 $a1 online resource (511 p.) 225 1 $aWiley classics library 300 $aDescription based upon print version of record. 311 $a0-471-68029-X 320 $aIncludes bibliographical references (p. 447-471) and indexes. 327 $aoptimal 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 327 $a3.6 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 327 $aChapter 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 327 $a6.6 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 327 $a8.1 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 327 $a9.1 Sufficient Statistics 330 $aThe Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. 410 0$aWiley classics library. 606 $aStatistical decision 606 $aBayesian statistical decision theory 608 $aElectronic books. 615 0$aStatistical decision. 615 0$aBayesian statistical decision theory. 676 $a519.8 700 $aDeGroot$b Morris H.$f1931-1989.$012496 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146070303321 996 $aOptimal statistical decisions$9117629 997 $aUNINA