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We propose a novel Bayesian methodology to mitigate misspecification andimprove estimating treatment effects. A plethora of methods to estimate --particularly the heterogeneous -- treatment effect have been proposed withvarying success. It is recognized, however, that the underlying data generatingmechanism, or even the model specification, can drastically affect theperformance of each method, without any way to compare its performance in realworld applications. Using a foundational Bayesian framework, we developBayesian causal synthesis; a supra-inference method that synthesizes severalcausal estimates to improve inference. We provide a fast posterior computationalgorithm and show that the proposed method provides consistent estimates ofthe heterogeneous treatment effect. Several simulations and an empirical studyhighlight the efficacy of the proposed approach compared to existingmethodologies, providing improved point and density estimation of theheterogeneous treatment effect.

Bayesian Causal Synthesis for Supra-Inference on Heterogeneous Treatment Effects