Elaboration of posteriori probability estimates for local inference in algebraic Bayesian networks in case of imprecise evidence

Abstract

For an algebraic Bayesian network, there are several degrees of consistency. In the case of a scalar representation of the probability the global consistency of the algorithms posteriori global output is proven. In the case of interval probability estimates the problem of obtaining consistent results is complicated by the need to use approximate methods to obtain estimates of the a posteriori probability. Results of the algorithms of local inference on the posterior interval estimates of the probabilities for all types of incoming evidence are analyzed. Additional restrictions in the case of imprecise evidence are proposed. The consistency of the resulting from global posteriori algorithm using these constraints network is proven.