The remainder of this paper is organized as follows. In Section 2, we recall the ingredients
of Bayesian networks and the task of structure discovery. Following the work of Buntine (1991),
Cooper and Herskovits (1992), and Friedman and Koller (2003) we, in Section 3, describe the
idea of conditioning by orders. Based on this, Section 4 presents a novel algorithm for averaging
over all network structures. In Section 5, we modify this algorithm to handle the maximization
problem. Possible extensions for large networks are sketched in Section 6. In Section 7, we provide
experimental results on four synthetic data sets. Finally, Section 8 concludes with a brief discussion.