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Gaussian process (GP) covariance function is proposed as a matching tool inGPMatch within a full Bayesian framework under relatively weaker causalassumptions. The matching is accomplished by utilizing GP prior covariancefunction to define matching distance. We show that GPMatch provides a doublyrobust estimate of the averaged treatment effect (ATE) much like theG-estimation, the ATE is correctly estimated when either conditions aresatisfied: 1) the GP mean function correctly specifies potential outcome\(Y^{(0)}\); or 2) the GP covariance function correctly specifies matchingstructure. Simulation studies were carried out without assuming any knownmatching structure nor functional form of the outcomes. The results demonstratethat GPMatch enjoys well calibrated frequentist properties, and outperformsmany widely used methods including Bayesian Additive Regression Trees. The casestudy compares effectiveness of early aggressive use of biological medicationin treating children with newly diagnosed Juvenile Idiopathic Arthritis, usingdata extracted from electronic medical records.

GPMatch: A Bayesian Doubly Robust Approach to Causal Inference with Gaussian Process Covariance Function As a Matching Tool