Algebraic Bayesian network primary structure transformation to an acyclic one that preserves its probabilistic semantics

The paper considers the given algebraic Bayesian network with interval probability estimates primary structure transformation to the primary structure of the network that is acyclic and stochastically equivalent to the given one. It is shown that this transformation only possible when hypergraph corresponding to the resulting primary structure comprises the hypergraph corresponding to the given one. We propose a method constructing probability estimates of the resulting primary structure, which makes it to be stochastically equivalent to the given one.