Bayesian Inference for Gaussian Mixed Graph Models
This work addresses the challenge of inferring causal effects in the presence of unmeasured confounding for researchers in statistics and causal inference, though it is incremental as it builds on existing graph models with new Bayesian methods.
The authors tackled the problem of performing Bayesian inference in Gaussian mixed graph models, which represent conditional independencies and arise from causal models with unmeasured confounding, by introducing priors and algorithms including Monte Carlo methods and a variational approximation to evaluate posterior distributions for quantities like causal effects.
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional independencies that is closed under marginalization and arises naturally from causal models which allow for unmeasured confounding. Monte Carlo methods and a variational approximation for such models are presented. Our algorithms for Bayesian inference allow the evaluation of posterior distributions for several quantities of interest, including causal effects that are not identifiable from data alone but could otherwise be inferred where informative prior knowledge about confounding is available.