J. Japan Statist. Soc., Vol. 31 (No. 2), pp. 175-185, 2001

The Graphical Condition for Identifying Arrows in Recovering Causal Structure

Manabu Kuroki, Tomoyoshi Kikuchi and Masami Miyakawa

Abstract. This paper deals with problems of recovering a causal structure by using not only conditional independence relationships but also prior knowledge when data are generated according to the causal structure among variables. Although some algorithms for recovering a causal structure based on independencies have been developed, the influence of prior knowledge on the recovery algorithms has not been clarified. In this paper, a necessary and sufficient condition for the existence of unidentified arrows in a recovered diagram is given in terms of graph structure. Also, it is shown that a causal structure such that a recovered diagram is a forest can be recovered by recognizing exogenous variables in a causal diagram completely. The result enables us to elucidate enough prior information to determine a causal diagram uniquely.

Key words and phrases: exogenous variable, faithfulness, maximally oriented pattern, observational equivalence, orientation rules, pattern.

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