A Bayesian approach to fusing uncertain, imprecise and conflicting information

The Dezert–Smarandache theory (DSmT) and transferable belief model (TBM) both address concerns with the Bayesian methodology as applied to applications involving the fusion of uncertain, imprecise and conflicting information. In this paper, we revisit these concerns regarding the Bayesian methodology in the light of recent developments in the context of the DSmT and TBM. We show that, by exploiting recent advances in the Bayesian research arena, one can devise and analyse Bayesian models that have the same emergent properties as DSmT and TBM. Specifically, we define Bayesian models that articulate uncertainty over the value of probabilities (including multimodal distributions that result from conflicting information) and we use a minimum expected cost criterion to facilitate making decisions that involve hypotheses that are not mutually exclusive. We outline our motivation for using the Bayesian methodology and also show that the DSmT and TBM models are computationally expedient approaches to achieving the same endpoint. Our aim is to provide a conduit between these two communities such that an objective view can be shared by advocates of all the techniques.