科学计算中的蒙特卡罗策略：英文版

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