Bayesian Causal Inference: A Tutorial

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Bayesian Causal inference : A TutorialFan LiDepartment of Statistical ScienceDuke UniversityJune 2, 2019Bayesian Causal inference Workshop, Ohio State UniversityCausationIRelevant questions about causationIthe philosophical meaningfulness of the notion of causationIdeducing the causes of a given effectIunderstanding details of a Causal mechanismIHere we focus on measuring the effects of causes, wherestatistics arguably can contribute mostISeveral statistical frameworksIgraphical models (S Wright, J Pearl)Istructural equations (S Wright, T Haavelmo, J Heckman)Ipotential outcomes (J Neyman, DB Rubin)Potential Outcome FrameworkIThe Potential Outcome Framework: the most widely usedframework across many disciplinesIBrief historyIRandomized experiments: Fisher (1918, 1925), Neyman(1923)IFormulation (assignment mechanism and Bayesian model):Rubin (1974, 1977, 1978)IObservational studies and propensity scores: Rosenbaumand Rubin (1983)IHeterogonous treatment effects and machine learning:Athey and Imbens (2015), many othersPotential Outcome Framework: Key ComponentsINo causation without mani

Strategy 1: Data Augmentation (Gibbs Sampling) I Imputation crucially depends onthe model for science: Pr(Yi(1);Yi(0)jXi) I But Yi(1);Yi(0) are never jointed observed, no information at all about the association between Yi(1) an Yi(0) ! posterior = prior, and posterior of estimand ˝will be sensitive to its prior

  Inference, Sampling, Casual, Gibbs, Causal inference, Gibbs sampling