Causal Inference: Combine Observational and Experimental Data
Experimental data and observational data are two distinct regimes of data used for causal inference, which have their strengths and weaknesses. In this project, we introduce a hyper-parameter to moderate the influence of the observational data through power likelihood. We propose using ELPD as a metric to select this hyperparameter. Through simulation studies, we show that our method effectively reduces the MSE of the Average Treatment Effect (ATE) estimate.