Causal Inference By Causal Networks

Causality-namely, our awareness of what causes what in the world and why it matters, is a significant concern in many scientific fields. Though it is basic to human thought, causality is a notion shrouded in mystery, controversy, and caution, because scientists and philosophers have had difficulties in defining cause and effect.Nevertheless, many scientists insist on studying causality. By far, the researches about causality are all based on a given model and some qualitative assumptions. The counterfactual or potential-outcomes model and the causal diagram are two important models for causal inference. In this paper, we study causality by intervention based on causal networks. An intervention is to force the values of some variables to change. An intervention may be complex in practice.In this paper, we first describe notation and definitions. Then, some conclusions about atomic intervention are given. And we describe how a causal network will change under a conditional intervention or a stochastic intervention. Then, we obtain some graphical criteria for identifying the causal effect of a conditional intervention or a stochastic intervention by an augmented graph after the intervention. When some criterion is satisfied, a simple closed-form expression is provided for the causal ef-fect of a conditional or stochastic intervention, which enables researchers to assess the causal effect with little effort. Assuming causal network with a Gaussian linear struc-tural equation model, the identification of causal effects is significant in epidemiology, clinical medicine, economics and so on. In this case, some results for path analysis are useful for identifying causal effects. In this circumstance, we study a special kind of conditional intervention. We introduce the double back-door criterion for identifica-tion and get the causal effects of a conditional intervention on the mean and variance of a response variable when the double back-door criterion is satisfied. Furthermore, we introduce an optimal conditional intervention. In general, selecting covariates sat-isfying the double back-door criterion is not unique. We give a graphical criterion for selecting covariates to identify the causal effect of an optimal conditional interven- tion. Assuming causal network with a Gaussian linear structural equation model, we study stochastic intervention and get the causal effects of a stochastic intervention on the mean and variance of a response variable when the back-door criterion is satisfied. Furthermore, we introduce an optimal stochastic intervention. In general, selecting co-variates satisfying the back-door criterion is not unique. We give a graphical criterion for selecting covariates to identify the causal effect of an optimal stochastic interven-tion. Furthermore, we consider the bounds on the average controlled direct effects (ACDEs) of a treatment variable on an unobserved response variable in the presence of unobserved confounders between an intermediate variable and the response vari-able. And we propose a graphical criterion for selecting variables caused by the re-sponse variable in order to derive the formulas for the bounds on the ACDEs. Finally, we propose a method for detecting confounder sets without knowledge of completely constructed causal networks.