Title: Dependent nonparametric priors for causal inference problems
Bayesian nonparametric methods have gained significant traction across various applied contexts,
with a notable surge in attention directed towards their applications in causal inference.
In this talk, we present two notable causal inference problems and demonstrate the valuable
impact of tailored dependent nonparametric priors. Both approaches employ dependent nonparametric
mixtures, which make a valuable contribution within the classical Rubin's missing potential outcome framework.
Firstly, we address the problem of estimating the conditional average treatment effect (CATE), introducing
a confounder-dependent mixture model to capture causal effect heterogeneity. Our method utilizes the flexibility of
a dependent Dirichlet process to model the distribution of potential outcomes conditioned on confounders.
This enables us to estimate individual treatment effects, identify distinct population groups with similar CATEs,
and estimate causal effects within each identified group. Secondly, we focus on principal stratification, a popular
concept in health and environmental sciences. However, when dealing with continuous post-treatment variables,
principal stratification poses several inferential challenges. One such challenge involves identifying latent
principal strata using information on the heterogeneous response of the intermediate variable to treatment.
Here, we leverage a dependent mixture prior with shared atoms to discover the principal strata and specifically
characterize the dissociative stratum, representing the stratum where no effect of the exposure is observed.
Both models are illustrated through applications analyzing the impact of pollution levels on health.
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