Extend transferable belief models with probabilistic priors

In this paper, we extend Smets' transferable belief model (TBM) with probabilistic priors. Our first motivation for the extension is about evidential reasoning when the underlying prior knowledge base is Bayesian. We extend standard Dempster models with prior probabilities to represent beliefs and distinguish between two types of induced mass functions on an extended Dempster model: one for believing and the other essentially for decision-making. There is a natural correspondence between these two mass functions. In the extended model, we propose two conditioning rules for evidential reasoning with probabilistic knowledge base. Our second motivation is about the partial dissociation of betting at the pignistic level from believing at the credal level in TBM. In our extended TBM, we coordinate these two levels by employing the extended Dempster model to represent beliefs at the credal level. Pignistic probabilities are derived not from the induced mass function for believing but from the one for decision-making in the model and hence need not rely on the choice of frame of discernment. Moreover, we show that the above two proposed conditionings and marginalization (or coarsening) are consistent with pignistic transformation in the extended TBM