Related papers: Quantifying knowledge with a new calculus for beli…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
In some real world information fusion situations, time critical decisions must be made with an incomplete information set. Belief function theories (e.g., Dempster-Shafer theory of evidence, Transferable Belief Model) have been shown to…
Mathematical Theory of Evidence called also Dempster-Shafer Theory (DST) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its…
The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as…
We construct the belief function that quantifies the agent, beliefs about which event of Q will occurred when he knows that the event is selected by a chance set-up and that the probability function associated to the chance set up is only…
Within the framework of evidence theory, the confidence functions of different information can be combined into a combined confidence function to solve uncertain problems. The Dempster combination rule is a classic method of fusing…
In real life, lots of information merges from time to time. To appropriately describe the actual situations, lots of theories have been proposed. Among them, Dempster-Shafer evidence theory is a very useful tool in managing uncertain…
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…
We give a probabilistic analysis of inductive knowledge and belief and explore its predictions concerning knowledge about the future, about laws of nature, and about the values of inexactly measured quantities. The analysis combines a…
Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences…
We describe a viewpoint on the Dempster/Shafer 'Theory of Evidence', and provide an interpretation which regards the combination formulas as statistics of the opinions of "experts". This is done by introducing spaces with binary operations…
Markov chain model is widely applied in many fields, especially the field of prediction. The classical Discrete-time Markov chain(DTMC) is a widely used method for prediction. However, the classical DTMC model has some limitation when the…
Some criticisms that have been raised against the Cox approach to probability theory are addressed. Should we use a single real number to measure a degree of rational belief? Can beliefs be compared? Are the Cox axioms obvious? Are there…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
This paper discusses how a measure of uncertainty representing a state of knowledge can be updated when a new information, which may be pervaded with uncertainty, becomes available. This problem is considered in various framework, namely:…
This paper presents two new promising rules of combination for the fusion of uncertain and potentially highly conflicting sources of evidences in the framework of the theory of belief functions in order to palliate the well-know limitations…
We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…
The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…