科学计算中的蒙特卡罗策略英文版 JUNS.LIU 著 2005年版

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资料名称：	科学计算中的蒙特卡罗策略英文版 JUNS.LIU 著 2005年版
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整理时间：	2023-11-06
软件简介：	科学计算中的蒙特卡罗策略英文版作者： JUNS.LIU 著出版时间：2005年版丛编项： Springer Series in Statistics 内容简介　　An early experiment that conceives the basic idea of Monte Carlo compu-tatios is known as "Buffon'needle"，first stated by Georges Louis Leclerc Comte de Buffon in 1777.In this well-known experiment，on throws a needle of length l onto a flat surface with a grid of parallel lines with spacing.It is easy to compute that，under ideal conditions，the chance that the needle will intersect one of the lines in .Thus，if we lep pN be the Proportion of "intersects"in N throws，we can have an estimate of π as wjocj will"converge"to π as N increases to infinity.此书为英文版！目录 Preface 1IntroductionandExamples 1.1TheNeedofMonteCarloTechniques 1.2ScopeandOutlineoftheBook 1.3ComputationsinStatisticalPhysics 1.4MolecularStructureSimulation 1.5Bioinformatics:FindingWeakRepetitivePatterns 1.6NonlinearDynamicSystem:TargetTracking 1.7HypothesisTestingforAstronomicalObservations 1.8BayesianInferenceofMultilevelModels 1.9MonteCarloandMissingDataProblems BasicPrinciples:Rejection,Weighting,andOthers 2.1GeneratingSimpleRandomVariables 2.2TheRejectionMethod 2.3VarianceReductionMethods 2.4ExactMethodsforChain-StructuredModels 2.4.1Dynamicprogramming 2.4.2Exactsimulation 2.5ImportanceSamplingandWeightedSample 2.5.1Anexample 2.5.2Thebasicidea 2.5.3The"ruleofthumb"forimportancesampling 2.5.4Conceptoftheweightedsample 2.5.5Marginalizationinimportancesampling 2.5.6Example:Solvingalinearsystem 2.5.7Example:ABayesianmissingdataproblem 2.6AdvancedImportanceSamplingTechniques 2.6.1Adaptiveimportancesampling 2.6.2Rejectionandweighting 2.6.3Sequentialimportancesampling 2.6.4Rejectioncontrolinsequentialimportancesampling 2.7ApplicationofSISinPopulationGenetics 2.8Problems TheoryofSequentialMonteCarlo 3.1EarlyDevelopments:GrowingaPolymer 3.1.1Asimplemodelofpolymer:Self-avoidwalk 3.1.2Growingapolymeronthesquarelattice 3.1.3Limitationsofthegrowthmethod 3.2SequentialImputationforStatisticalMissingDataProblems 3.2.1Likelihoodcomputation 3.2.2Bayesiancomputation 3.3NonlinearFiltering 3.4AGeneralFramework 3.4.1Thechoiceofthesamplingdistribution 3.4.2Normalizingconstant 3.4.3Pruning,enrichment,andresampling 3.4.4Moreaboutresampling 3.4.5Partialrejectioncontrol 3.4.6Marginalization,look-ahead,anddelayedestimate 3.5Problems SequentialMonteCarloinAction 4.1SomeBiologicalProblems 4.1.1MolecularSimulation 4.1.2Inferenceinpopulationgenetics 4.1.3FindingmotifpatternsinDNAsequences 4.2ApproximatingPermanents 4.3Counting0-1TableswithFixedMargins 4.4BayesianMissingDataProblems 4.4.1Murray'sdata 4.4.2NonparametricBayesanalysisofbinomialdata 4.5ProblemsinSignalProcessing 4.5.1TargettrackinginclutterandmixtureKalmanfilter 4.5.2Digitalsignalextractioninfadingchannels 4.6Problems MetropolisAlgorithmandBeyond 5.1TheMetropolisAlgorithm 5.2MathematicalFormulationandHastings'sGeneralization 5.3WhyDoestheMetropolisAlgorithmWork? 5.4SomeSpecialAlgorithms 5.4.1Random-walkMetropolis 5.4.2Metropolizedindependencesampler 5.4.3ConfigurationalbiasMonteCarlo 5.5MultipointMetropolisMethods 5.5.1Multipleindependentproposals 5.5.2Correlatedmultipointproposals 5.6ReversibleJumpingRule 5.7DynamicWeighting 5.8OutputAnalysisandAlgorithmEfficiency 5.9Problems TheGibbsSampler 6.1GibbsSamplingAlgorithms 6.2IllustrativeExamples 6.3SomeSpecialSamplers 6.3.1Slicesampler 6.3.2MetropolizedGibbssampler 6.3.3Hit-and-runalgorithm 6.4DataAugmentationAlgorithm 6.4.1Bayesianmissingdataproblem 6.4.2TheoriginalDAalgorithm 6.4.3ConnectionwiththeGibbssampler 6.4.4Anexample:HierarchicalBayesmodel 6.5FindingRepetitiveMotifsinBiologicalSequences 6.5.1AGibbssamplerfordetectingsubtlemotifs 6.5.2Alignmentandclassification 6.6CovarianceStructuresoftheGibbsSampler 6.6.1DataAugmentation 6.6.2Autocovariancesfortherandom-scanGibbssampler 6.6.3MoreefficientuseofMonteCarlosamples 6.7CollapsingandGroupinginaGibbsSampler 6.8Problems 7ClusterAlgorithmsfortheIsingModel 7.1IsingandPottsModelRevisit 7.2TheSwendsen-WangAlgorithmasDataAugmentation 7.3ConvergenceAnalysisandGeneralization 7.4TheModificationbyWolff 7.5FurtherGeneralization 7.6Discussion 7.7Problems GeneralConditionalSampling 8.1PartialResampling 8.2CaseStudiesforPartialResampling 8.2.1Gaussianrandomfieldmodel 8.2.2Texturesynthesis 8.2.3Inferencewithmultivariatet-distribution 8.3TransformationGrSupandGeneralizedGibbs 8.4Application:ParameterExpansionforDataAugmentation 8.5SomeExamplesinBayesianInference 8.5.1Probitregression 8.5.2MonteCarlobridgingforstochasticdifferentialequa-tion 8.6Problems 9MolecularDynamicsandHybridMonteCarlo 9.1BasicsofNewtonianMechanics 9.2MolecularDynamicsSimulation 9.3HybridMonteCarlo 9.4AlgorithmsRelatedtoHMC 9.4.1Langevin-Eulermoves 9.4.2GeneralizedhybridMonteCarlo 9.4.3Surrogatetransitionmethod 9.5MultipointStrategiesforHybridMonteCarlo 9.5.1Neal'swindowmethod 9.5.2Multipointmethod 9.6ApplicationofHMCinStatistics 9.6.1Indirectobservationmodel 9.6.2Estimationinthestochasticvolatilitymodel 10MultilevelSamplingandOptimizationMethods 10.1UmbrellaSampling 10.2SimulatedAnnealing 10.3SimulatedTempering 10.4ParallelTempering 10.5GeneralizedEnsembleSimulation 10.5.1Multicanonicalsampling 10.5.2The1/k-ensemblemethod 10.5.3Comparisonofalgorithms 10.6TemperingwithDynamicWeighting 10.6.1Isingmodelsimulationatsub-criticaltemperature 10.6.2Neuralnetworktraining 11Population-BasedMonteCarloMethods 11.1AdaptiveDirectionSampling:SnookerAlgorithm 11.2ConjugateGradientMonteCarlo 11.3EvolutionaryMonteCarlo 11.3.1Evolutionarymovementsinbinary-codedspace 11.3.2Evolutionarymovementsincontinuousspace 11.4SomeFurtherThoughts 11.5NumericalExamples 11.5.1Simulatingfromabimodaldistribution 11.5.2Comparingalgorithmsforamultimodalexample 11.5.3Variableselectionwithbinary-codedEMC 11.5.4Bayesianneuralnetworktraining 11.6Problems 12MarkovChainsandTheirConvergence 12.1BasicPropertiesofaMarkovChain 12.1.1Chapman-Kolmogorovequation 12.1.2Convergencetostationarity 12.2CouplingMethodforCardShuffling 12.2.1Random-to-topshuffling 12.2.2Riffleshuffling 12.3ConvergenceTheoremforFinite-StateMarkovChains 12.4CouplingMethodforGeneralMarkovChain 12.5GeometricInequalities 12.5.1Basicsetup 12.5.2Poincareinequality 12.5.3Example:Simplerandomwalkonagraph 12.5.4Cheeger'sinequality 12.6FunctionalAnalysisforMarkovChains 12.6.1Forwardandbackwardoperators 12.6.2ConvergencerateofMarkovchains 12.6.3Maximalcorrelation 12.7BehavioroftheAverages 13SelectedTheoreticalTopics 13.1MCMCConvergenceandConvergenceDiagnostics 13.2IterativeConditionalSampling 13.2.1Dataaugmentation 13.2.2Random-scanGibbssampler 13.3ComparisonofMetropolis-TypeAlgorithms 13.3.1Peskun'sordering 13.3.2ComparingschemesusingPeskun'sordering 13.4EigenvalueAnalysisfortheIndependenceSampler 13.5PerfectSimulation 13.6ATheoryforDynamicWeighting 13.6.1Definitions 13.6.2Weightbehaviorunderdifferentscenarios 13.6.3Estimationwithweightedsamples 13.6.4Asimulationstudy ABasicsinProbabilityandStatistics A.1BasicProbabilityTheory A.1.1Experiments,events,andprobability A.1.2Univariaterandomvariablesandtheirproperties A.1.3Multivariaterandomvariable A.1.4Convergenceofrandomvariables A.2StatisticalModelingandInference A.2.1Parametricstatisticalmodeling A.2.2Frequentistapproachtostatisticalinference A.2.3Bayesianmethodology A.3BayesProcedureandMissingDataFormalism A.3.1Thejointandposteriordistributions A.3.2Themissingdataproblem A.4TheExpectation-MaximizationAlgorithm References AuthorIndex SubjectIndex111
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