| The usefulness of Bayesian networks in representing knowledge with uncertainty is widely accepted. A Bayesian network consists of a qualitative part a directed acyclic graph (DAG) and a quantitative part a collection of numerical parameters, which are usually conditional probability tables. Bayesian networks also admit a natural causal interpretation, and therefore they are a kind of language in which causal concepts can be discussed and analyzed in precise terms. This dissertation concerns the problem of identifying casual effects in causal Bayesian networks. Causal effects enable us to predict how systems respond to external interventions without carrying out controlled experiments. Based on the work of other researchers, especially Tian and Pearl, we offer a sound and complete algorithm to solve the identification problem on general causal Bayesian networks. Our result shows the power of the algebraic approach in solving identifiability problems and closes the identifiability problem of unconditional interventions. We recognize that the graphical and transformational approach to identifiability questions proposed by other researchers has certain advantages over the algebraic approach in terms of ease of explanation. The most important graphical approach to identifiability is the do-calculus method given by J. Pearl. We prove that it is complete, in the sense that, if a causal effect is identifiable, there exists a sequence of applications of the rules of the do-calculus that transforms the causal effect formula into a formula that only includes observational quantities. Our result confirms Pearl's conjecture of the completeness property of his method, which had been stated in 1995. |
