Local computations in Dempster-Shafer theory of evidence

When applying any technique of multidimensional models to problems of practice, one always has to cope with two problems: it is necessary to have a possibility to represent the models with a “reasonable” number of parameters and to have sufficiently efficient computational procedures at one’s disposal. When considering graphical Markov models in probability theory, both of these conditions are fulfilled; various computational procedures for decomposable models are based on the ideas of local computations, whose theoretical foundations were laid by Lauritzen and Spiegelhalter. The presented contribution studies a possibility of transferring these ideas from probability theory into Dempster-Shafer theory of evidence. The paper recalls decomposable models, discusses connection of the model structure with the corresponding system of conditional independence relations, and shows that under special additional conditions, one can locally compute specific basic assignments which can be considered to be conditional.