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蒙特卡罗统计方法

作者: [法] 罗伯特著

出版社: 世界图书出版公司

出版时间: 2009-10

版次: 2

ISBN: 9787510005114

定价: 79.00

装帧: 平装

开本: 16开

纸张: 胶版纸

页数: 645页

正文语种: 英语

分类: 自然科学

1 张插图图片

　　Itisatributetoourprofessionthatatextbookthatwascurrentin1999isstartingtofeelold.TheworkforthefirsteditionofMonteCarloStatisticalMethods(MCSM1)wasfinishedinlate1998,andtheadvancesmadesincethen,aswellasourlevelofunderstandingofMonteCarlomethods,havegrownagreatdeal.Moreover,twootherthingshavehappened.TopicsthatjustmadeitintoMCSM1withthebriefesttreatment(forexample,perfectsampling)havenowattainedalevelofimportancethatnecessitatesamuchmorethoroughtreatment.Secondly,someothermethodshavenotwithstoodthetestoftimeor,perhaps,havenotyetbeenfullydeveloped,andnowreceiveamoreappropriatetreatment.
　　WhenweworkedonMCSM1inthemid-to-late90s,MCMCalgorithmswerealreadyheavilyused,andtheflowofpublicationsonthistopicwasatsuchahighlevelthatthepicturewasnotonlyrapidlychanging,butalsonecessarilyincomplete.Thus,theprocessthatwefollowedinMCSM1wasthatofsomeonewhowasthrownintotheoceanandwastryingtograbontothebiggestandmostseeminglyusefulobjectswhiletryingtoseparatetheflotsamfromthejetsam.Nonetheless,wealsofeltthatthefundamentalsofmanyofthesealgorithmswereclearenoughtobecoveredatthetextbookalevel,sowe"swamon. 作者：(法国)罗伯特(ChristianP.Robert)(法国)GeorgeCasella PrefacetotheSecondEdition
PrefacetotheFirstEdition
1Introduction
1.1StatisticalModels
1.2LikelihoodMethods
1.3BayesianMethods
1.4DeterministicNumericalMethods
1.4.1Optimization
1.4.2Integration
1.4.3Comparison
1.5Problems
1.6Notes
1.6.1PriorDistributions
1.6.2BootstrapMethods

2RandomVariableGeneration
2.1Introduction
2.1.1UniformSimulation
2.1.2TheInverseTransform
2.1.3Alternatives
2.1.4OptimalAlgorithms
2.2GeneralTransformationMethods
2.3Accept-RejectMethods
2.3.1TheFundamentalTheoremofSimulation
2.3.2TheAccept-RejectAlgorithm
2.4EnvelopeAccept-RejectMethods
2.4.1TheSqueezePrinciple
2.4.2Log-ConcaveDensities
2.5Problems
2.6Notes
2.6.1TheKissGenerator
2.6.2Quasi-MonteCarloMethods
2.6.3MixtureRepresentatiOnS

3MonteCarloIntegration
3.1IntroduCtion
3.2ClassicalMonteCarloIntegration
3.3ImportanceSampling
3.3.1Principles
3.3.2FiniteVarianceEstimators
3.3.3ComparingImportanceSamplingwithAccept-Reject
3.4LaplaceApproximations
3.5Problems
3.6Notes
3.6.1LargeDeviationsTechniques
3.6.2TheSaddlepointApproximation

4ControlingMonteCarloVariance
4.1MonitoringVariationwiththeCLT
4.1.1UnivariateMonitoring
4.1.2MultivariateMonitoring
4.2Rao-Blackwellization
4.3RiemannApproximations
4.4AccelerationMethods
4.4.1AntitheticVariables
4.4.2Contr01Variates
4.5Problems
4.6Notes
4.6.1MonitoringImportanceSamplingConvergence
4.6.2Accept-RejectwithLooseBounds
4.6.3Partitioning

5MonteCarloOptimization
5.1Introduction
5.2StochasticExploration
5.2.1ABasicSolution
5.2.2GradientMethods
5.2.3SimulatedAnnealing
5.2.4PriorFeedback
5.3StochasticApproximation
5.3.1MissingDataModelsandDemarginalization
5.3.2ThcEMAlgorithm
5.3.3MonteCarloEM
5.3.4EMStandardErrors
5.4Problems
5.5Notes
5.5.1VariationsonEM
5.5.2NeuralNetworks
5.5.3TheRobbins-Monroprocedure
5.5.4MonteCarloApproximation

6MarkovChains
6.1EssentialsforMCMC
6.2BasicNotions
6.3Irreducibility，Atoms，andSmallSets
6.3.1Irreducibility
6.3.2AtomsandSmallSets
6.3.3CyclesandAperiodicity
6.4TransienceandRecurrence
6.4.1ClassificationofIrreducibleChains
6.4.2CriteriaforRecurrence
6.4.3HarrisRecurrence
6.5InvariantMeasures
6.5.1StationaryChains
6.5.2Kac’sTheorem
6.5.3ReversibilityandtheDetailedBalanceCondition
6.6ErgodicityandConvergence
6.611Ergodicity
6.6.2GeometricConvergence
6.6.3UniformErgodicity
6.7LimitTheorems
6.7.1ErgodicTheorems
6.7.2CentralLimitTheorems
6.8Problems
6.9Notes
6.9.1Dri允Conditions
6.9.2Eaton’SAdmissibilityCondition
6.9.3AlternativeConvergenceConditions
6.9.4MixingConditionsandCentralLimitTheorems
6.9.5CovarianceinMarkovChains

7TheMetropolis-HastingsAlgorithm
7.1TheMCMCPrinciple
7.2MonteCarloMethodsBasedonMarkovChains
7.3TheMetropolis-Hastingsalgorithm
7.3.1Definition
7.3.2ConvergenceProperties
7.4TheIndependentMetropolis-HastingsAlgorithm
7.4.1FixedProposals
7.4.2AMetropolis-HastingsVersionofARS
7.5Randomwalks
7.6OptimizationandContr01
7.6.1OptimizingtheAcceptanceRate
7.6.2ConditioningandAccelerations
7.6.3AdaptiveSchemes
7.7Problems
7.8Nores
7.8.1BackgroundoftheMetropolisAlgorithm
7.8.2GeometricConvergenceofMetropolis-HastingsAlgorithms
7.8.3AReinterpretationofSimulatedAnnealing
7.8.4RCferenceAcceptanceRates
7.8.5LangevinAlgorithms

8TheSliceSampler
8.1AnotherLookattheFundamentalTheorem
8.2TheGeneralSliceSampler
8.3ConvergencePropertiesoftheSliceSampler
8.4Problems
8.5Notes
8.5.1DealingwithDi伍cultSlices

9TheTwo－StageGibbsSampler
9.1AGeneralClassofTwo-StageAlgorithms
9.1.1FromSliceSamplingtoGibbsSampling
9.1.2Definition
9.1.3BacktotheSliceSampler
9.1.4TheHammersley-CliffordTheorem
9.2FundamentalProperties
9.2.1ProbabilisticStructures
9.2.2ReversibleandInterleavingChains
9.2.3TheDualityPrinciple
9.3MonotoneCovarianceandRao-Btackwellization
9.4TheEM-GibbsConnection
9.5Transition
9.6Problems
9.7Notes
9.7.1InferenceforMixtures
9.7.2ARCHModels

10TheMulti-StageGibbsSampler
10.1BasicDerivations
10.1.1Definition
10.1.2Completion
……
11VariableDimensionModelsandReversibleJumpAlgorithms
12DiagnosingConvergence
13PerfectSampling
14IteratedandSequentialImportanceSampling
AProbabilityDistributions
BNotation
References
IndexofNames
IndexofSubjects
内容简介:
　　Itisatributetoourprofessionthatatextbookthatwascurrentin1999isstartingtofeelold.TheworkforthefirsteditionofMonteCarloStatisticalMethods(MCSM1)wasfinishedinlate1998,andtheadvancesmadesincethen,aswellasourlevelofunderstandingofMonteCarlomethods,havegrownagreatdeal.Moreover,twootherthingshavehappened.TopicsthatjustmadeitintoMCSM1withthebriefesttreatment(forexample,perfectsampling)havenowattainedalevelofimportancethatnecessitatesamuchmorethoroughtreatment.Secondly,someothermethodshavenotwithstoodthetestoftimeor,perhaps,havenotyetbeenfullydeveloped,andnowreceiveamoreappropriatetreatment.
　　WhenweworkedonMCSM1inthemid-to-late90s,MCMCalgorithmswerealreadyheavilyused,andtheflowofpublicationsonthistopicwasatsuchahighlevelthatthepicturewasnotonlyrapidlychanging,butalsonecessarilyincomplete.Thus,theprocessthatwefollowedinMCSM1wasthatofsomeonewhowasthrownintotheoceanandwastryingtograbontothebiggestandmostseeminglyusefulobjectswhiletryingtoseparatetheflotsamfromthejetsam.Nonetheless,wealsofeltthatthefundamentalsofmanyofthesealgorithmswereclearenoughtobecoveredatthetextbookalevel,sowe"swamon.
作者简介:
作者：(法国)罗伯特(ChristianP.Robert)(法国)GeorgeCasella
目录:
PrefacetotheSecondEdition
PrefacetotheFirstEdition
1Introduction
1.1StatisticalModels
1.2LikelihoodMethods
1.3BayesianMethods
1.4DeterministicNumericalMethods
1.4.1Optimization
1.4.2Integration
1.4.3Comparison
1.5Problems
1.6Notes
1.6.1PriorDistributions
1.6.2BootstrapMethods

2RandomVariableGeneration
2.1Introduction
2.1.1UniformSimulation
2.1.2TheInverseTransform
2.1.3Alternatives
2.1.4OptimalAlgorithms
2.2GeneralTransformationMethods
2.3Accept-RejectMethods
2.3.1TheFundamentalTheoremofSimulation
2.3.2TheAccept-RejectAlgorithm
2.4EnvelopeAccept-RejectMethods
2.4.1TheSqueezePrinciple
2.4.2Log-ConcaveDensities
2.5Problems
2.6Notes
2.6.1TheKissGenerator
2.6.2Quasi-MonteCarloMethods
2.6.3MixtureRepresentatiOnS

3MonteCarloIntegration
3.1IntroduCtion
3.2ClassicalMonteCarloIntegration
3.3ImportanceSampling
3.3.1Principles
3.3.2FiniteVarianceEstimators
3.3.3ComparingImportanceSamplingwithAccept-Reject
3.4LaplaceApproximations
3.5Problems
3.6Notes
3.6.1LargeDeviationsTechniques
3.6.2TheSaddlepointApproximation

4ControlingMonteCarloVariance
4.1MonitoringVariationwiththeCLT
4.1.1UnivariateMonitoring
4.1.2MultivariateMonitoring
4.2Rao-Blackwellization
4.3RiemannApproximations
4.4AccelerationMethods
4.4.1AntitheticVariables
4.4.2Contr01Variates
4.5Problems
4.6Notes
4.6.1MonitoringImportanceSamplingConvergence
4.6.2Accept-RejectwithLooseBounds
4.6.3Partitioning

5MonteCarloOptimization
5.1Introduction
5.2StochasticExploration
5.2.1ABasicSolution
5.2.2GradientMethods
5.2.3SimulatedAnnealing
5.2.4PriorFeedback
5.3StochasticApproximation
5.3.1MissingDataModelsandDemarginalization
5.3.2ThcEMAlgorithm
5.3.3MonteCarloEM
5.3.4EMStandardErrors
5.4Problems
5.5Notes
5.5.1VariationsonEM
5.5.2NeuralNetworks
5.5.3TheRobbins-Monroprocedure
5.5.4MonteCarloApproximation

6MarkovChains
6.1EssentialsforMCMC
6.2BasicNotions
6.3Irreducibility，Atoms，andSmallSets
6.3.1Irreducibility
6.3.2AtomsandSmallSets
6.3.3CyclesandAperiodicity
6.4TransienceandRecurrence
6.4.1ClassificationofIrreducibleChains
6.4.2CriteriaforRecurrence
6.4.3HarrisRecurrence
6.5InvariantMeasures
6.5.1StationaryChains
6.5.2Kac’sTheorem
6.5.3ReversibilityandtheDetailedBalanceCondition
6.6ErgodicityandConvergence
6.611Ergodicity
6.6.2GeometricConvergence
6.6.3UniformErgodicity
6.7LimitTheorems
6.7.1ErgodicTheorems
6.7.2CentralLimitTheorems
6.8Problems
6.9Notes
6.9.1Dri允Conditions
6.9.2Eaton’SAdmissibilityCondition
6.9.3AlternativeConvergenceConditions
6.9.4MixingConditionsandCentralLimitTheorems
6.9.5CovarianceinMarkovChains

7TheMetropolis-HastingsAlgorithm
7.1TheMCMCPrinciple
7.2MonteCarloMethodsBasedonMarkovChains
7.3TheMetropolis-Hastingsalgorithm
7.3.1Definition
7.3.2ConvergenceProperties
7.4TheIndependentMetropolis-HastingsAlgorithm
7.4.1FixedProposals
7.4.2AMetropolis-HastingsVersionofARS
7.5Randomwalks
7.6OptimizationandContr01
7.6.1OptimizingtheAcceptanceRate
7.6.2ConditioningandAccelerations
7.6.3AdaptiveSchemes
7.7Problems
7.8Nores
7.8.1BackgroundoftheMetropolisAlgorithm
7.8.2GeometricConvergenceofMetropolis-HastingsAlgorithms
7.8.3AReinterpretationofSimulatedAnnealing
7.8.4RCferenceAcceptanceRates
7.8.5LangevinAlgorithms

8TheSliceSampler
8.1AnotherLookattheFundamentalTheorem
8.2TheGeneralSliceSampler
8.3ConvergencePropertiesoftheSliceSampler
8.4Problems
8.5Notes
8.5.1DealingwithDi伍cultSlices

9TheTwo－StageGibbsSampler
9.1AGeneralClassofTwo-StageAlgorithms
9.1.1FromSliceSamplingtoGibbsSampling
9.1.2Definition
9.1.3BacktotheSliceSampler
9.1.4TheHammersley-CliffordTheorem
9.2FundamentalProperties
9.2.1ProbabilisticStructures
9.2.2ReversibleandInterleavingChains
9.2.3TheDualityPrinciple
9.3MonotoneCovarianceandRao-Btackwellization
9.4TheEM-GibbsConnection
9.5Transition
9.6Problems
9.7Notes
9.7.1InferenceforMixtures
9.7.2ARCHModels

10TheMulti-StageGibbsSampler
10.1BasicDerivations
10.1.1Definition
10.1.2Completion
……
11VariableDimensionModelsandReversibleJumpAlgorithms
12DiagnosingConvergence
13PerfectSampling
14IteratedandSequentialImportanceSampling
AProbabilityDistributions
BNotation
References
IndexofNames
IndexofSubjects

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蒙特卡罗统计方法

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