Covariate selection for identifying the causal effects of stochastic interventions using causal networks

Suppose that cause–effect relationships between variables can be described by a causal network corresponding to a linear structural equation model. Kuroki and Miyakawa (2003) proposed a graphical criterion for selecting covariates to identify the causal effect of a conditional intervention. In this paper, we extend Kuroki and Miyakawa (2003) graphical criterion for selecting covariates to identify the causal effect of a stochastic intervention. Since stochastic intervention is a generalization of conditional intervention, our paper makes the results of Kuroki and Miyakawa (2003) more generally applicable.