Bayesian Inference for Gaussian Mixed Graph Models

TL;DR

This paper develops Bayesian inference methods for Gaussian mixed graph models, enabling estimation of causal effects with unmeasured confounding using priors, Monte Carlo, and variational algorithms.

Contribution

It introduces priors and algorithms for Bayesian inference in Gaussian acyclic mixed graph models, facilitating causal inference with unmeasured confounding.

Findings

Monte Carlo and variational algorithms for inference

Posterior evaluation of causal effects with priors

Applicable to models with unmeasured confounding

Abstract

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.