Causal Inference in Statistics: A Primer

159 Pages·2016·1.45 MB·English

by  Judea Pearl

(cid:2)
CAUSAL INFERENCE
IN STATISTICS
(cid:2) (cid:2)
(cid:2)
(cid:2)
(cid:2) (cid:2)
(cid:2)
(cid:2)
CAUSAL INFERENCE
IN STATISTICS
A PRIMER
JudeaPearl
ComputerScienceandStatistics,UniversityofCalifornia,
LosAngeles,USA
MadelynGlymour
Philosophy,CarnegieMellonUniversity,Pittsburgh,USA
NicholasP.Jewell
BiostatisticsandStatistics,UniversityofCalifornia,
(cid:2) (cid:2)
Berkeley,USA
(cid:2)
(cid:2)
Thiseditionfirstpublished2016
©2016JohnWiley&SonsLtd
Registeredoffice
JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom
Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyfor
permissiontoreusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com.
TherightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththeCopyright,
DesignsandPatentsAct1988.
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inany
formorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUK
Copyright,DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher.
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbe
availableinelectronicbooks.
Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnamesand
productnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheir
respectiveowners.Thepublisherisnotassociatedwithanyproductorvendormentionedinthisbook.
LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsinpreparing
thisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontentsof
thisbookandspecificallydisclaimanyimpliedwarrantiesofmerchantabilityorfitnessforaparticularpurpose.Itis
soldontheunderstandingthatthepublisherisnotengagedinrenderingprofessionalservicesandneitherthe
publishernortheauthorshallbeliablefordamagesarisingherefrom.Ifprofessionaladviceorotherexpert
assistanceisrequired,theservicesofacompetentprofessionalshouldbesought.
(cid:2) (cid:2)
LibraryofCongressCataloging-in-PublicationDataappliedfor
ISBN:9781119186847
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
CoverImage:©gmaydos/Getty
Typesetin10/12ptTimesLTStdbySPiGlobal,Chennai,India
1 2016
(cid:2)
(cid:2)
To my wife, Ruth, my greatest mentor.
– Judea Pearl
To my parents, who are the causes of me.
– Madelyn Glymour
To Debra and Britta, who inspire me every day.
– Nicholas P. Jewell
(cid:2) (cid:2)
(cid:2)
(cid:2)
(cid:2) (cid:2)
(cid:2)
(cid:2)
Contents
AbouttheAuthors ix
Preface xi
ListofFigures xv
AbouttheCompanionWebsite xix
1 Preliminaries:StatisticalandCausalModels 1
1.1 WhyStudyCausation 1
1.2 Simpson’sParadox 1
(cid:2) 1.3 ProbabilityandStatistics 7 (cid:2)
1.3.1 Variables 7
1.3.2 Events 8
1.3.3 ConditionalProbability 8
1.3.4 Independence 10
1.3.5 ProbabilityDistributions 11
1.3.6 TheLawofTotalProbability 11
1.3.7 UsingBayes’Rule 13
1.3.8 ExpectedValues 16
1.3.9 VarianceandCovariance 17
1.3.10 Regression 20
1.3.11 MultipleRegression 22
1.4 Graphs 24
1.5 StructuralCausalModels 26
1.5.1 ModelingCausalAssumptions 26
1.5.2 ProductDecomposition 29
2 GraphicalModelsandTheirApplications 35
2.1 ConnectingModelstoData 35
2.2 ChainsandForks 35
2.3 Colliders 40
2.4 d-separation 45
2.5 ModelTestingandCausalSearch 48
(cid:2)
(cid:2)
viii Contents
3 TheEffectsofInterventions 53
3.1 Interventions 53
3.2 TheAdjustmentFormula 55
3.2.1 ToAdjustornottoAdjust? 58
3.2.2 MultipleInterventionsandtheTruncatedProductRule 60
3.3 TheBackdoorCriterion 61
3.4 TheFront-DoorCriterion 66
3.5 ConditionalInterventionsandCovariate-SpecificEffects 70
3.6 InverseProbabilityWeighing 72
3.7 Mediation 75
3.8 CausalInferenceinLinearSystems 78
3.8.1 StructuralversusRegressionCoefficients 80
3.8.2 TheCausalInterpretationofStructuralCoefficients 81
3.8.3 IdentifyingStructuralCoefficientsandCausalEffect 83
3.8.4 MediationinLinearSystems 87
4 CounterfactualsandTheirApplications 89
4.1 Counterfactuals 89
4.2 DefiningandComputingCounterfactuals 91
4.2.1 TheStructuralInterpretationofCounterfactuals 91
4.2.2 TheFundamentalLawofCounterfactuals 93
4.2.3 FromPopulationDatatoIndividualBehavior–AnIllustration 94
4.2.4 TheThreeStepsinComputingCounterfactuals 96
(cid:2) (cid:2)
4.3 NondeterministicCounterfactuals 98
4.3.1 ProbabilitiesofCounterfactuals 98
4.3.2 TheGraphicalRepresentationofCounterfactuals 101
4.3.3 CounterfactualsinExperimentalSettings 103
4.3.4 CounterfactualsinLinearModels 106
4.4 PracticalUsesofCounterfactuals 107
4.4.1 RecruitmenttoaProgram 107
4.4.2 AdditiveInterventions 109
4.4.3 PersonalDecisionMaking 111
4.4.4 SexDiscriminationinHiring 113
4.4.5 MediationandPath-disablingInterventions 114
4.5 MathematicalToolKitsforAttributionandMediation 116
4.5.1 AToolKitforAttributionandProbabilitiesofCausation 116
4.5.2 AToolKitforMediation 120
References 127
Index 133
(cid:2)