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统计决策理论和贝叶斯分析（第2版）

统计决策理论和贝叶斯分析（第2版）
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作者: 著
出版社: 世界图书出版公司
2004-11
版次: 1
ISBN: 9787506271813
定价: 88.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 617页
分类: 自然科学
125人买过
  • 　　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. 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
  • 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
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