The General Expression of the Prior Convergence Error: A Proof

In [2], we introduced the notion of the parental synergy. In the same paper, moreover, an expression was advanced for the prior convergence error (the error which is found in the marginal probabilities computed for a node when the parents of this node are wrongfully assumed to be independent), in which the parental synergy has a key position as weighting factor. This key position suggests that the parental synergy captures a fundamental feature of a Bayesian network. In this paper a proof is provided for the correctness of the conjectured expression of the prior convergence error.