Matrix-vector algorithms of global posteriori inference in algebraic Bayesian networks

Algorithm of global posteriori inference in algebraic Bayesian networks is considered in the paper. The results obtained earlier for local a posteriori inference are briefly presented. Main steps of global propagation algorithm are described in details. A transition matrix from the vector of knowledge pattern elements to the virtual evidence, propagated to the next knowledge pattern, is proposed. The stated theorem describes the matrix-vector representation of the stochastic evidence propagation algorithm within a network with scalar estimates of the knowledge patterns elements probabilities of truth. The obtained results form the basis for development of the global posteriori inference machine matrix-vector representation in algebraic Bayesian networks and simplify its further software implementation.