Algebraic Bayesian network: non-linear optimization problem in local posteriori inference with atomic stochastic evidence

Recalculation of an existing truth probability estimates given the probability of incoming evidence constutes the second problem of posterior inference in algebraic Bayesian networks. We consider the analysis of non-linear optimization problem arising from the atomic stochastic evidence propagation in the knowledge pattern with interval estimations. Conversion to enclosing interval boarders estimates allows one to reduce the non-linear optimization problem to series of quadratic or hyperbolic mathematical programming problems