Bayesian Causal Inference in Probit Graphical Models

We consider a binary response which is potentially affected by set of continuous variables. Of special interest the causal effect on due to an intervention specific variable. The latter can be meaningfully determined basis observational data through suitable assumptions generating mechanism. In particular we assume that joint distribution obeys conditional independencies (Markov properties) inherent in Directed Acyclic Graph (DAG), and DAG given interpretation notion interventional distribution. propose DAG-probit model where generated discretization random threshold latent variable latter, jointly with remaining variables, has belonging zero-mean Gaussian whose covariance matrix constrained satisfy Markov properties DAG; assigned DAG-Wishart prior corresponding Cholesky parameters. Our leads natural definition conditionally DAG. Since generates observations unknown, present efficient MCMC algorithm target posterior space DAGs, parameters concentration matrix, linking latent. end result Bayesian Model Averaging estimate incorporates parameter, as well model, uncertainty. methodology assessed using simulation experiments applied gene expression originating from breast cancer stem cells.