A Bayesian Approach to Learning Causal Networks
  Whereas acausal Bayesian networks represent probabilistic independence,
causal Bayesian networks represent causal relationships. In this paper, we
examine Bayesian methods for learning both types of networks. Bayesian methods
for learning acausal networks are fairly well developed. These methods often
employ assumptions to facilitate the construction of priors, including the
assumptions of parameter independence, parameter modularity, and likelihood
equivalence. We show that although these assumptions also can be appropriate
for learning causal networks, we need additional assumptions in order to learn
causal networks. We introduce two sufficient assumptions, called {em mechanism
independence} and {em component independence}. We show that these new
assumptions, when combined with parameter independence, parameter modularity,
and likelihood equivalence, allow us to apply methods for learning acausal
networks to learn causal networks.
