A Study Of Identifiability In Causal Bayesian Networks Version 0.3

This paper addresses the problem of identifying causal effects from nonex-perimental data in a causal Bayesian network, i.e., a directed acyclic graph thatrepresents causal relationships. The identifiability question asks whether itis possible to compute the probability of some set of (effect) variables givenintervention on another set of (intervention) variables, in the presence of non-observable (i.e., hidden or latent) variables. It is well known that the answer tothe question depends on the structure of the causal Bayesian network, the setof observable variables, the set of effect variables, and the set of interventionvariables. Our work is based on the work of Tian and Pearl [1, 2, 3] and ourownwork [4], and extends it. We show that the identify algorithm that Tian andPearl define and prove sound for semi-Markovian models can be transfered togeneral causal graphs and is not only sound, but also complete. This resulteffectively solves the identifiability question for causal Bayesian networks thatPearl posed in 1995 [5], by providing a sound and complete algorithm for iden-tifiability.