Decision-making in distributed sensor networks: A belief-theoretic Bayes-like theorem

A Dempster-Shafer (DS) belief theoretic evidence updating strategy is ideally suited to accommodate the difficulties associated with the availability of only incomplete information at each node of a distributed sensor network (DSN). Such a strategy however must also account for sensor heterogeneity, 'inertia' and 'integrity' of the existing knowledge base and reliability of the data generated at each sensor node. In this paper, we propose a Bayes-like theorem that can conveniently address these issues while allowing one to compute the 'posterior' belief of a 'hypothesis' given an 'observation' when the corresponding 'likelihoods' and 'priors' are available. Unlike previous work on DS belief theoretic generalizations of Bayes' theorem, our work is based on the Fagin-Halpern conditional notions that can be considered more 'natural extensions' of corresponding Bayesian notions.