  Scientists often use directed acyclic graphs (days) to model the qualitative
structure of causal theories, allowing the parameters to be estimated from
observational data. Two causal models are equivalent if there is no experiment
which could distinguish one from the other. A canonical representation for
causal models is presented which yields an efficient graphical criterion for
deciding equivalence, and provides a theoretical basis for extracting causal
structures from empirical data. This representation is then extended to the
more general case of an embedded causal model, that is, a dag in which only a
subset of the variables are observable. The canonical representation presented
here yields an efficient algorithm for determining when two embedded causal
models reflect the same dependency information. This algorithm leads to a model
theoretic definition of causation in terms of statistical dependencies.
