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Frequentist inference has a well-established supporting theory for doubly robust causal inference based on the potential outcomes framework, which is realized via outcome regression (OR) and propensity score (PS) models. The Bayesian counterpart, however, is not obvious as the PS model loses its balancing property in joint modeling. In this paper, we propose a natural and formal Bayesian solution by bridging loss-type Bayesian inference with a utility function derived from the notion of a pseudo-population via the change of measure. Consistency of the posterior distribution is shown with correctly specified and misspecified OR models. Simulation studies suggest that our proposed method can estimate the true causal effect more efficiently and achieve the frequentist coverage if either the OR model is correctly specified or fit with a flexible function of the confounders, compared to the previous Bayesian approach via the Bayesian bootstrap. Finally, we apply this novel Bayesian method to assess the impact of speed cameras on the reduction of car collisions in England.
The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and testing tho
This paper derives time-uniform confidence sequences (CS) for causal effects in experimental and observational settings. A confidence sequence for a target parameter $psi$ is a sequence of confidence intervals $(C_t)_{t=1}^infty$ such that every one
Due to concerns about parametric model misspecification, there is interest in using machine learning to adjust for confounding when evaluating the causal effect of an exposure on an outcome. Unfortunately, exposure effect estimators that rely on mach
This study proposes a new Bayesian approach to infer binary treatment effects. The approach treats counterfactual untreated outcomes as missing observations and infers them by completing a matrix composed of realized and potential untreated outcomes
A large number of statistical models are doubly-intractable: the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means that standard inference techniq