A Comparison of Bayesian and Belief Function Reasoning

Abstract

The goal of this paper is to compare the similarities and differences between Bayesian and belief function reasoning. Our main conclusion is that although there are obvious differences in semantics, representations, the rules for combining and marginalizing representations, there are many similarities. We claim that the two calculi have roughly the same expressive power. Each calculus has its own semantics that allow us to construct models suited for these semantics. Once we have a model in either calculus, one can transform it to the other by means of a suitable transformation.

Prioritization Assessment for Capability Gaps in Weapon System of Systems Based on the Conditional Evidential Network

“…The inverse conditional likelihood belief is calculated via the GBT theorem using Equations (9) and (10). The obtained reverse conditional likelihood belief has the joint form Pl(Pa(C)|C) for the lower multiple capabilities and must be marginalized.…”

Game-Theoretical Semantics of Epistemic Probability Transformations

“…Originally developed by Voorbraak [29] as a probabilistic approximation intended to limit the computational cost of operating with belief functions in the Dempster-Shafer framework, the plausibility transform [5] ∑ y∈Θ pl b (y) . We call the outputpl b of the plausibility transform relative plausibility of singletons.…”

A Geometric Approach to the Theory of Evidence

“…In estimation problems, for instance, it is often required to compute a point-wise estimate of the quantity of interest: object tracking [12] is a typical example. The problem of approximating a belief function with a probability then naturally arises [13], [14], [15], [16], [17], [18], [19], [20], [21]. The link between b.f.s and probabilities is as well the foundation of a popular approach to the theory of evidence, Smets' "transferable belief model" [22].…”