In this paper we prove that a recent Bayesian approximation of belief functions, the relative belief of singletons, meets a number of properties with respect to Dempster’s rule of combination which mirrors those satisfied by the relative plausibility of singletons. In particular, the related operator commutes with Dempster’s sum of plausibility functions, while the relative belief perfectly rep...

Hierarchical Bayesian modeling provides a flexible and interpretable way of extending simple models of cognitive processes. To introduce this special issue, we discuss four of the most important potential hierarchical Bayesian contributions. The first involves the development of more complete theories, including accounting for variation coming from sources like individual differences in cogniti...

Bayesian theory [5] is one of the most commonly utilized theories for managing uncertainty in information fusion [20, 12]. The theory relies on two main assumptions: (1) a probability function should be used for representing belief and (2) Bayes’ theorem should be used for belief updating when a new observation has been made. The main criticism of Bayesian theory that can be found in the litera...