统计决策理论和贝叶斯分析（第2版）

图书标准信息

• 作者 JamesO.Berger 著
• 出版社 世界图书出版公司
• 出版时间 2004-11
• 版次 1
• ISBN 9787506271813
• 定价 88.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 617页

【内容简介】

　　Therelationships（bothconceptualandmathematical）betweenBayesiananalysisandstatisticaldecisiontheoryaresostrongthatitissomewhatunnaturaltolearnonewithouttheother.Nevertheless,majorportionsofeachhavedevelopedseparately.OntheBayesianside,thereisanextensivelydevelopedBayesiantheoryofstatisticalinference（bothsubjectiveandobjectiveversions）.Thistheoryrecognizestheimportanceofviewingstatisticalanalysisconditionally（i.e.,treatingobserveddataasknownratherthanunknown）,evenwhennolossfunctionistobeincorporatedintotheanalysis.Thereisalsoawell-developed（frequentist）decisiontheory,whichavoidsformalutilizationofpriordistributionsandseekstoprovideafoundationforfrequentiststatisticaltheory.AlthoughthecentralthreadofthebookwillbeBayesiandecisiontheory,bothBayesianinferenceandnon-Bayesiandecisiontheorywillbeextensivelydiscussed.Indeed,thebookiswrittensoastoallow,say,theteachingofacourseoneithersubjectseparately.

【目录】

CHAPTER1
BasicConcepts
1.1Introduction
1.2BasicElements
1.3ExpectedLoss,DecisionRules,andRisk
1.3.1BayesianExpectedLoss
1.3.2FrequentistRisk
1.4RandomizedDecisionRules
1.5DecisionPrinciples
1.5.1TheConditionalBayesDecisionPrinciple
1.5.2FrequentistDecisionPrinciples
1.6Foundations
1.6.1MisuseofClassicalInferenceProcedures
1.6.2TheFrequentistPerspective
1.6.3TheConditionalPerspective
1.6.4TheLikelihoodPrinciple
1.6.5ChoosingaParadigmorDecisionPrinciple
1.7SufficientStatistics
1.8Convexity
Exercises
CHAPTER2　UtilityandLoss
2.1Introduction
2.2UtilityTheory
2.3TheUtilityofMoney
2.4TheLossFunction
2.4.1DevelopmentfromUtilityTheory
2.4.2CertainStandardLossFunctions
2.4.3ForInferenceProblems
2.4.4ForPredictiveProblems
2.4.5VectorValuedLossFunctions
2.5Criticisms
Exercises
CHAPTER3　PriorInformationandSubjectiveProbability
3.1SubjectiveProbability
3.2SubjectiveDeterminationofthePriorDensity
3.3NoninformativePriors
3.3.1Introduction
3.3.2NoninformativePriorsforLocationandScaleProblems
3.3.3NoninformativePriorsinGeneralSettings
3.3.4Discussion
3.4MaximumEntropyPriors
3.5UsingtheMarginalDistributiontoDeterminethePrior
3.5.1TheMarginalDistribution
3.5.2InformationAbouttn
3.5.3RestrictedClassesofPriors
3.5.4TheML-IIApproachtoPriorSelection
3.5.5TheMomentApproachtoPriorSelection
3.5.6TheDistanceApproachtoPriorSelection
3.5.7MarginalExchangeability
3.6HierarchicalPriors
3.7Criticisms
3.8TheStatisticiansRole
Exercises
CHAPTER4　BayesianAnalysis
4.1Introduction
4.2ThePosteriorDistribution
4.2.1DefinitionandDetermination
4.2.2ConjugateFamilies
4.2.3ImproperPriors
4.3BayesianInference
4.3.1Estimation
4.3.2CredibleSets
4.3.3HypothesisTesting
4.3.4PredictiveInference
4.4BayesianDecisionTheory
4.4.1PosteriorDecisionAnalysis
4.4.2Estimation
4.4.3FiniteActionProblemsandHypothesisTesting
4.4.4WithInferenceLosses
4.5EmpiricalBayesAnalysis
4.5.1Introduction
4.5.2PEBForNormalMeans--TheExchangeableCase
4.5.3PEBForNormalMeans--TheGeneralCase
4.5.4NonparametricEmpiricalBayesAnalysis
4.6HierarchicalBayesAnalysis
4.6.1Introduction
4.6.2ForNormalMeans--TheExchangeableCase
4.6.3ForNormalMeans--TheGeneralCase
4.6.4ComparisonwithEmpiricalBayesAnalysis
4.7BayesianRobustness
4.7.1Introduction
4.7.2TheRoleoftheMarginalDistribution
4.7.3PosteriorRobustness:BasicConcepts
4.7.4PosteriorRobustness:s-ContaminationClass
4.7.5BayesRiskRobustnessandUseofFrequentistMeasures
4.7.6Gamma-MinimaxApproach
4.7.7UsesoftheRiskFunction
4.7.8SomeRobustandNonrobustSituations
4.7.9RobustPriors
4.7.10RobustPriorsforNormalMeans
4.7.11OtherIssuesinRobustness
4.8AdmissibilityofBayesRulesandLongRunEvaluations
4.8.1AdmissibilityofBayesRules
4.8.2AdmissibilityofGeneralizedBayesRules
4.8.3InadmissibilityandLongRunEvaluations
4.9BayesianCalculation
4.9.1NumericalIntegration
4.9.2MonteCarloIntegration
4.9.3AnalyticApproximations
4.10BayesianCommunication
4.10.1Introduction
4.10.2AnIllustration:TestingaPointNullHypothesis
4.11CombiningEvidenceandGroupDecisions
4.11.1CombiningProbabilisticEvidence
4.11.2CombiningDecision-TheoreticEvidence
4.11.3GroupDecisionMaking
4.12Criticisms
4.12.1Non-BayesianCriticisms
4.12.2FoundationalCriticisms
Exercises
CHAPTER5　MinimaxAnalysis
5.1Introduction
5.2GameTheory
5.2.1BasicElements
5.2.2GeneralTechniquesforSolvingGames
5.2.3FiniteGames
5.2.4GameswithFinite
5.2.5TheSupportingandSeparatingHyperplaneTheorems
5.2.6TheMinimaxTheorem
5.3StatisticalGames
5.3.1Introduction
5.3.2GeneralTechniquesforSolvingStatisticalGames
5.3.3StatisticalGameswithFinite
5.4ClassesofMinimaxEstimators
5.4.1Introduction
5.4.2TheUnbiasedEstimatorofRisk
5.4.3MinimaxEstimatorsofaNormalMeanVector
5.4.4MinimaxEstimatorsofPoissonMeans
5.5EvaluationoftheMinimaxPrinciple
5.5.1AdmissibilityofMinimaxRules
5.5.2RationalityandtheMinimaxPrinciple
5.5.3ComparisonwiththeBayesianApproach
5.5.4TheDesiretoActConservatively
5.5.5MinimaxRegret
5.5.6Conclusions
Exercises
CHAPTER6　Invariance
6.1Introduction
6.2Formulation
6.2.1GroupsofTransformations
6.2.2InvariantDecisionProblems
6.2.3InvariantDecisionRules
6.3LocationParameterProblems
6.4OtherExamplesofInvariance
6.5Maximallnvariants
6.6InvarianceandNoninformativePriors
6.6.1RightandLeftInvariantHaarDensities
6.6.2TheBestInvariantRule
6.6.3ConfidenceandCredibleSets
6.7InvarianceandMinimaxity
6.8AdmissibilityofInvariantRules
6.9Conclusions
Exercises
CHAPTER7　PreposteriorandSequentialAnalysis
7.1Introduction
7.2OptimalFixedSampleSize
7.3SequentialAnalysis--Notation
7.4BayesianSequentialAnalysis
7.4.1Introduction
7.4.2Notation
7.4.3TheBayesDecisionRule
7.4.4ConstantPosteriorBayesRisk
7.4.5TheBayesTruncatedProcedure
7.4.6LookAheadProcedures
7.4.7InnerTruncation
7.4.8ApproximatingtheBayesProcedureandtheBayesRisk
7.4.9TheoreticalResults
7.4.10OtherTechniquesforFindingaBayesProcedure
7.5TheSequentialProbabilityRatioTest
7.5.1TheSPRTasaBayesProcedure
7.5.2ApproximatingthePowerFunctionandtheExpectedSampleSize
7.5.3AccuracyoftheWaldApproximations
7.5.4BayesRiskandAdmissibility
7.5.5OtherUsesoftheSPRT
7.6MinimaxSequentialProcedures
7.7TheEvidentialRelevanceoftheStoppingRule
7.7.1Introduction
7.7.2TheStoppingRulePrinciple
7.7.3PracticalImplications
7.7.4CriticismsoftheStoppingRulePrinciple
7.7.5InformativeStoppingRules
7.8DiscussionofSequentialLossFunctions
Exercises
CHAPTER8　CompleteandEssentiallyCompleteClasses
8.1Preliminaries
8.2CompleteandEssentiallyCompleteClassesfromEarlierChapters
8.2.1DecisionRulesBasedonaSufficientStatistic
8.2.2NonrandomizedDecisionRules
8.2.3FiniteO
8.2.4TheNeyman-PearsonLemma
8.3One-SidedTesting
8.4MonotoneDecisionProblems
8.4.1MonotoneMultipleDecisionProblems
8.4.2MonotoneEstimationProblems
8.5LimitsofBayesRules
8.6OtherCompleteandEssentiallyCompleteClassesofTests
8.6.1Two-SidedTesting
8.6.2HigherDimensionalResults
8.6.3SequentialTesting
8.7CompleteandEssentiallyCompleteClassesinEstimation
8.7.1GeneralizedBayesEstimators
8.7.2IdentifyingGeneralizedBayesEstimators
8.8ContinuousRiskFunctions
8.9ProvingAdmissibilityandInadmissibility
8.9.1SteinsNecessaryandSufficientConditionforAdmissibility
8.9.2ProvingAdmissibility
8.9.3ProvingInadmissibility
8.9.4MinimalorNearlyMinimalCompleteClasses
Exercises
APPENDIX1　CommonStatisticalDensities
IContinuous
IIDiscrete
APPENDIX2　SupplementtoChapter4
IDefinitionandPropertiesofHm
IIDevelopmentof（4.121）and（4.122）
IIIVerificationofFormula（4.123）
APPENDIX3　TechnicalArgumentsfromChapter7
IVerificationofFormula（7.8）
IIVerificationofFormula（7.10）
Bibliography
NotationandAbbreviations
AuthorIndex
SubjectIndex