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The motivation for this paper is the geometric approach to statistical learning Bayesiannetwork (BN) structures. We review three vector encodings of BN structures. The first one hasbeen used by Jaakkola et al.  and also by Cussens , the other two use special integral vectorsformerly introduced, called imsets [18, 20]. The topic is the comparison of outer polyhedral approximationsof the corresponding polytopes. We show how to transform the inequalities suggested byJaakkola et al.  intodoi:10.18409/jas.v4i1.19 fatcat:o7752omvvvgmvkxtziiu6g6q5e