In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of ‘‘quantum theory from five reasonable axioms.’’ Here we show that Hardy’s first axiom, which identifies probability with limiting frequency in an ensemble, is not necessary for his derivation. By reformulating Hardy’s assumptions, and modifying a part of his proof, in terms of Bayesian probabilities, we show that his ...

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

Abstract Gaussian Process based Bayesian Optimization is largely adopted for solving problems where the inputs are in Euclidean spaces. In this paper we associate to discrete probability distributions which elements of simplex. To search new design space, need a distance between distributions. The optimal transport (aka Wasserstein distance) chosen due its mathematical structure and computation...

This paper deals with the use of Bayesian networks to compute system reliability. The reliability analysis problem is described and the usual methods for quantitative reliability analysis are presented within a case study. Some drawbacks that justify the use of Bayesian networks are identified. The basic concepts of the Bayesian networks application to reliability analysis are introduced and a ...

Dempster-Shafer evidence theory is an efficient mathematical tool to deal with uncertain information. In that theory, basic probability assignment (BPA) is the basic element for the expression and inference of uncertainty. Decision-making based on BPA is still an open issue in Dempster-Shafer evidence theory. In this paper, a novel approach of transforming basic probability assignments to proba...

Savage denied that Bayesian decision theory applies in large worlds. This paper proposes a minimal extension of Bayesian decision theory to a large-world context that evaluates an event E by assigning it a number π(E) that reduces to an orthodox probability for a class of measurable events. The Hurwicz criterion evaluates π(E) as a weighted arithmetic mean of its upper and lower probabilities, ...

Probabilistic graphical models such as Bayesian Networks are one of the most powerful structures known by the Computer Science community for deriving probabilistic inferences. However, modern cognitive psychology has revealed that human decisions could not follow the rules of classical probability theory, because humans cannot process large amounts of data in order to make judgements. Consequen...

Statistical analysis of multinomial counts with a large number K of categories and a small number n of sample size is challenging to both frequentist and Bayesian methods and requires thinking about statistical inference at a very fundamental level. Following the framework of Dempster-Shafer theory of belief functions, a probabilistic inferential model is proposed for this “large K and small n”...