The study of the interplay between belief and probability has recently been posed in a geometric framework, in which belief and plausibility functions are represented as points of simplices in a Cartesian space. All Bayesian approximations of a belief function b form two homogeneous groups, which we call “affine” and “epistemic” families. In this paper, in particular, we focus on relative plaus...

In recent years, Bayesian learning models have been applied to an increasing variety of domains. While such models have been criticized on theoretical grounds, the underlying assumptions and predictions are rarely made concrete and tested experimentally. Here, I use Frank and Tenenbaum's (2011) Bayesian model of rule-learning as a case study to spell out the underlying assumptions, and to confr...

We present a general framework for representing belief-revision rules and use it to characterize Bayes’s rule as a classical example and Je¤rey’s rule as a non-classical one. In Je¤rey’s rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes’s rule, but a new assignment of probabilities to some events. Despite their di¤erences, Bayes’s and J...

Computational models of learning have proved largely successful in characterizing potential mechanisms which allow humans to make decisions in uncertain and volatile contexts. We report here findings that extend existing knowledge and show that a modified reinforcement learning model, which has separate parameters according to whether the previous trial gave a reward or a punishment, can provid...

Several schemes have been proposed for compactly representing multiattribute utility functions, yet none seems to achieve the level of success achieved by Bayesian and Markov models for probability distributions. In an attempt to bridge the gap, we propose a new representation for utility functions which follows its probabilistic analog to a greater extent. Starting from a simple definition of ...

This paper explores the impact of the assumption of unambiguous types on the Dempster-Shafer equilibrium introduced by Eichberger and Kelsey (2004). It is shown that if the types of the Sender are perceived unambiguous, then the Receiver’s conditional Choquet preference derived by the DempsterShafer updating rule is expected utility, regardless of whether the observed massage is ambiguous or no...

This paper characterizes several belief-revision rules in a uni…ed framework: Bayesian revision upon learning some event, Je¤rey revision upon learning new probabilities of some events, Adams revision upon learning some new conditional probabilities, and ‘dual-Je¤rey’revision upon learning a new conditional probability function. Despite their di¤erences, these revision rules can be characterize...

In the application of discriminant analysis, a situation sometimes arises where individual measurements are screened by a multidimensional screening scheme. For this situation, a discriminant analysis with screened populations is considered from a Bayesian viewpoint, and an optimal predictive rule for the analysis is proposed. In order to establish a flexible method to incorporate the prior inf...

In a recent paper [1] we introduced the Fuzzy Bayesian Learning (FBL) paradigm where expert opinions can be encoded in the form of fuzzy rule bases and the hyper-parameters of the fuzzy sets can be learned from data using a Bayesian approach. The present paper extends this work for selecting the most appropriate rule base among a set of competing alternatives, which best explains the data, by c...

This paper introduces a new algorithm called “Adaptive Multimodal Biometric Fusion Algorithm”(AMBF), which is a combination of Bayesian decision fusion and particle swarm optimization. A Bayesian framework is implemented to fuse decisions received from multiple biometric sensors. The system’s accuracy improves for a subset of decision fusion rules. The optimal rule is a function of the error co...