导语

  

内容提要

  

    这是一部被广泛认可的关于贝叶斯方法的最领先的读本，因为其易于理解、分析数据和解决研究问题的实际操作性强而广受赞誉。贝叶斯数据分析，第三版应用最新的贝叶斯方法，继续采用实用的方法来分析数据。作者均是统计界的领导人物，在呈现更高等的方法之前，从数据分析的观点引进基本概念。整本书从始至终，从实际应用和研究中提取的大量的练习实例强调了贝叶斯推理在实践中的应用。

Preface
Part1:FundamentalsofBayesian1nference
  1  Probabilityandinference
    1.1  ThethreestepsofBayesiandataanalysis
    1.2  Generalnotationforstatisticalinference
    1.3  Bayesianinference
    1.4  Discreteexamples:geneticsandspellchecking
    1.5  Probabilityasameasureofuncertainty
    1.6  Example:probabilitiesfromfootballpointspreads
    1.7  Example:calibrationforrecordlinkage
    1.8  Someusefulresultsfromprobabilitytheory
    1.9  Computationandsoftware
    1.10  Bayesianinferenceinappliedstatistics
    1.11  Bibliographicnote
    1.12  Exercises
  2  Single-parametermodels
    2.1  Estimatingaprobabilityfrombinomialdata
    2.2  Posteriorascompromisebetweendataandpriorinformation
    2.3  Summarizingposteriorinference
    2.4  1nformativepriordistributions
    2.5  Normaldistributionwithknownvariance
    2.6  Otherstandardsingle-parametermodels
    2.7  Example:informativepriordistributionforcancerrates
    2.8  Noninformativepriordistributions
    2.9  Weaklyinformativepriordistributions
    2.10  Bibliographicnote
    2.11  Exercises
  3  1ntroductiontomultiparametermodels
    3.1  Averagingover'nuisanceparameters'
    3.2  Normaldatawithanoninformativepriordistribution
    3.3  Normaldatawithaconjugatepriordistribution
    3.4  Multinomialmodelforcategoricaldata
    3.5  Multivariatenormalmodelwithknownvariance
    3.6  Multivariatenormalwithunknownmeanandvariance
    3.7  Example:analysisofabioassayexperiment
    3.8   Summaryofelementarymodelingandcomputation
    3.9  Bibliographicnote
    3.10  Exercises
  4  Asymptoticsandconnectionstonon-Bayesianapproaches
    4.1  Normalapproximationstotheposteriordistribution
    4.2  Large-sampletheory
    4.3  Counterexamplestothetheorems
    4.4  FrequencyevaluationsofBayesianinferences
    4.5  Bayesianinterpretationsofotherstatisticalmethods
    4.6  Bibliographicnote
    4.7  Exercises
  5  Hierarchicalmodels
    5.1  Constructingaparameterizedpriordistribution
    5.2  Exchangeabilityandhierarchicalmodels
    5.3  Bayesiananalysisofconjugatehierarchicalmodels
    5.4  Normalmodelwithexchangeableparameters
    5.5  Example:parallelexperimentsineightschools
    5.6  Hierarchicalmodelingappliedtoameta-analysis
    5.7  Weaklyinformativepriorsforvarianceparameters
    5.8  Bibliographicnote
    5.9  Exercises
Part11:FundamentalsofBayesianDataAnalysis
  6  Modelchecking
    6.1  TheplaceofmodelcheckinginappliedBayesianstatistics
    6.2  Dotheinferencesfromthemodelmakesense?
    6.3  Posteriorpredictivechecking
    6.4  Graphicalposteriorpredictivechecks
    6.5  Modelcheckingfortheeducationaltestingexample
    6.6  Bibliographicnote
    6.7  Exercises
  7  Evaluating，comparing，andexpandingmodels
    7.1  Measuresofpredictiveaccuracy
    7.2  1nformationcriteriaandcross-validation
    7.3  Modelcomparisonbasedonpredictiveperformance
    7.4  ModelcomparisonusingBayesfactors
    7.5  Continuousmodelexpansion
    7.6  1mplicitassumptionsandmodelexpansion:anexample
    7.7  Bibliographicnote
    7.8  Exercises
  8  Modelingaccountingfordatacollection
    8.1  Bayesianinferencerequiresamodelfordatacollection
    8.2  Data-collectionmodelsandignorability
    8.3  Samplesurveys
    8.4  Designedexperiments
    8.5  Sensitivityandtheroleofrandomization
    8.6  Observationalstudies
    8.7  Censoringandtruncation
    8.8  Discussion
    8.9  Bibliographicnote
    8.10  Exercises
  9  Decisionanalysis
    9.1  Bayesiandecisiontheoryindifferentcontexts
    9.2  Usingregressionpredictions:surveyincentives
    9.3  Multistagedecisionmaking:medicalscreening
    9.4  Hierarchicaldecisionanalysisforhomeradon
    9.5  Personalvs.institutionaldecisionanalysis
    9.6  Bibliographicnote
    9.7  Exercises
Part111:AdvancedComputation
  10  1ntroductiontoBayesiancomputation
    10.1  Numericalintegration
    10.2  Distributionalapproximations
    10.3  Directsimulationandrejectionsampling
    10.4  1mportancesampling
    10.5  Howmanysimulationdrawsareneeded?
    10.6  Computingenvironments
    10.7  DebuggingBayesiancomputing
    10.8  Bibliographicnote
    10.9  Exercises
  11  BasicsofMarkovchainsimulation
    11.1  Gibbssampler
    11.2  MetropolisandMetropolis-Hastingsalgorithms
    11.3  UsingGibbsandMetropolisasbuildingblocks
    11.4  1nferenceandassessingconvergence
    11.5  Effectivenumberofsimulationdraws
    11.6  Example:hierarchicalnormalmodel
    11.7  Bibliographicnote
    11.8  Exercises
  12  ComputationallyefficientMarkovchainsimulation
    12.1  EfficientGibbssamplers
    12.2  EfficientMetropolisjumpingrules
    12.3  FurtherextensionstoGibbsandMetropolis
    12.4  HamiltonianMonteCarlo
    12.5  HamiltonianMonteCarloforahierarchicalmodel
    12.6  Stan:developingacomputingenvironment
    12.7  Bibliographicnote
    12.8  Exercises
  13  Modalanddistributionalapproximations
    13.1  Findingposteriormodes
    13.2  Boundary-avoidingpriorsformodalsummaries
    13.3  Normalandrelatedmixtureapproximations
    13.4  FindingmarginalposteriormodesusingEM
    13.5  Conditionalandmarginalposteriorapproximations
    13.6  Example:hierarchicalnormalmodel（continued）
    13.7  Variationalinference
    13.8  Expectationpropagation
    13.9  Otherapproximations
    13.10  Unknownnormalizingfactors
    13.11 Bibliographicnote
    13.12  Exercises
Part1V:RegressionModels
  14  1ntroductiontoregressionmodels
    14.1  Conditionalmodeling
    14.2  Bayesiananalysisofclassicalregression
    14.3  Regressionforcausalinference:incumbencyandvoting
    14.4  Goalsofregressionanalysis
    14.5  Assemblingthematrixofexplanatoryvariables
    14.6  Regularizationanddimensionreduction
    14.7  Unequalvariancesandcorrelations
    14.8  1ncludingnumericalpriorinformation
    14.9  Bibliographicnote
    14.10  Exercises
  15  Hierarchicallinearmodels
    15.1  Regressioncoefficientsexchangeableinbatches
    15.2  Example:forecastingU.S.presidentialelections
    15.3  1nterpretinganormalpriordistributionasextradata
    15.4  Varyinginterceptsandslopes
    15.5  Computation:batchingandtransformation
    15.6  Analysisofvarianceandthebatchingofcoefficients
    15.7  Hierarchicalmodelsforbatchesofvariancecomponents
    15.8  Bibliographicnote
    15.9  Exercises
  16  Generalizedlinearmodels
    16.1  Standardgeneralizedlinearmodellikelihoods
    16.2  Workingwithgeneralizedlinearmodels
    16.3  Weaklyinformativepriorsforlogisticregression
    16.4  OverdispersedPoissonregressionforpolicestops
    16.5  State-levelopinonsfromnationalpolls
    16.6  Modelsformultivariateandmultinomialresponses
    16.7  Loglinearmodelsformultivariatediscretedata
    16.8  Bibliographicnote
    16.9  Exercises
  17  Modelsforrobustinference
    17.1  Aspectsofrobustness
    17.2  Overdispersedversionsofstandardmodels
    17.3  Posteriorinferenceandcomputation
    17.4  Robustinferencefortheeightschools
    17.5  Robustregressionusingt-distributederrors
    17.6  Bibliographicnote
    17.7  Exercises
  18  Modelsformissingdata
    18.1  Notation
    18.2  Multipleimputation
    18.3  Missingdatainthemultivariatenormalandtmodels
    18.4  Example:multipleimputationforaseriesofpolls
    18.5  Missingvalueswithcounteddata
    18.6  Example:anopinionpollinSlovenia
    18.7  Bibliographicnote
    18.8  Exercises
PartV:NonlinearandNonparametricModels
  19  Parametricnonlinearmodels
    19.1  Example:serialdilutionassay
    19.2  Example:populationtoxicokinetics
    19.3  Bibliographicnote
    19.4  Exercises
  20  Basisfunctionmodels
    20.1  Splinesandweightedsumsofbasisfunctions
    20.2  Basisselectionandshrinkageofcoefficients
    20.3  Non-normalmodelsandregressionsurfaces
    20.4  Bibliographicnote
    20.5  Exercises
  21  Gaussianprocessmodels
    21.1  Gaussianprocessregression
    21.2  Example:birthdaysandbirthdates
    21.3  LatentGaussianprocessmodels
    21.4  Functionaldataanalysis
    21.5  Densityestimationandregression
    21.6  Bibliographicnote
    21.7  Exercises
  22  Finitemixturemodels
    22.1  Settingupandinterpretingmixturemodels
    22.2  Example:reactiontimesandschizophrenia
    22.3  Labelswitchingandposteriorcomputation
    22.4  Unspecifiednumberofmixturecomponents
    22.5  Mixturemodelsforclassificationandregression
    22.6  Bibliographicnote
    22.7  Exercises
  23  Dirichletprocessmodels
    23.1  Bayesianhistograms
    23.2  Dirichletprocesspriordistributions
    23.3  Dirichletprocessmixtures
    23.4  Beyonddensityestimation
    23.5  Hierarchicaldependence
    23.6  Densityregression
    23.7  Bibliographicnote
    23.8  Exercises
Appendixes
  A  Standardprobabilitydistributions
    A.1  Continuousdistributions
    A.2  Discretedistributions
    A.3  Bibliographicnote
  B  Outlineofproofsoflimittheorems
    B.1  Bibliographicnote
  C  ComputationinRandStan
    C.1  GettingstartedwithRandStan
    C.2  FittingahierarchicalmodelinStan
    C.3  Directsimulation，Gibbs，andMetropolisinR
    C.4  ProgrammingHamiltonianMonteCarloinR
    C.5  Furthercommentsoncomputation
    C.6  Bibliographicnote
References
Author 1ndex
Subject 1ndex