Semiparametric Bayesian causal inference
Kolyan Ray, Aad van der Vaart
Abstract
We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently, we estimate the causal effect of a treatment, correcting nonparametrically for confounding. We show that standard Gaussian process priors satisfy a semiparametric Bernstein–von Mises theorem under smoothness conditions. We further propose a novel propensity score-dependent prior that provides efficient inference under strictly weaker conditions. We also show that it is theoretically preferable to model the covariate distribution with a Dirichlet process or Bayesian bootstrap, rather than modelling its density.
Topics & Concepts
Dirichlet processMathematicsCovariateBayesian probabilitySemiparametric regressionEconometricsPrior probabilityBayesian inferenceCausal inferenceInferenceDirichlet distributionGaussian processSemiparametric modelSmoothnessComputer scienceMixture modelStatisticsHierarchical Dirichlet processFrequentist inferenceCausal modelBayesian averageArtificial intelligenceWiener processBayesian statisticsMarkov chain Monte CarloPropensity score matchingStatistical inferenceGaussianAdvanced Causal Inference TechniquesBayesian Modeling and Causal InferenceStatistical Methods and Inference