科学计算中的蒙特卡罗策略 英文版 JUNS.LIU 著 2005年版

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