Bayesian causal estimation via model misspecification

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With an increasing amount of observational data becoming available, there is a pressing need to use appropriate statistical models to answer meaningful causal questions. Causal inference is widely studied across all sciences, such as public transportation and epidemiology. The inference target is a causal estimand which measures the change in the expected outcome of unit under study of different interventions. It has a well-established basis in frequentist semi-parametric theory, with estimation of causal parameters typically conducted via outcome regression and propensity score adjustment. A Bayesian counterpart, however, is not obvious as doubly robust estimation involves a semi-parametric formulation in the absence of a fully specified likelihood function. In this project, we aim to investigate solutions for Bayesian causal inference from standard prior-to-posterior updating, without requiring a parametric family for the observations, and also robust to model misspecfication. We will apply the propose methods to evaluate and quantify London's Stop & Search causal effects on deterring drug offenses in previous decade.