On the semi-Markov Equivalence of Causal Models

The variability of structure in a finite Markov equivalence class of causally sufficient mod­ els represented by directed acyclic graphs has been fully characterized. Without causal suf­ ficiency, an infinite semi-Markov equivalence class of models has only been characterized by the fact that each model in the equiva­ lence class entails the same marginal statis­ tical dependencies. In this paper, we study the variability of structure of causal models within a semi-Markov equivalence class and propose a systematic approach to construct models entailing any specific marginal statis­ tical dependencies.