Related papers: A correlation coefficient of belief functions
This paper is concerned with the apparent greatest weakness of the Mathematical Theory of Evidence (MTE) of Shafer \cite{Shafer:76}, which has been strongly criticized by Wasserman \cite{Wasserman:92ijar}. Weaknesses of Shafer's proposal…
Knowing when a classifier's prediction can be trusted is useful in many applications and critical for safely using AI. While the bulk of the effort in machine learning research has been towards improving classifier performance,…
Dissimilar notions of quantum correlations have been established, each being motivated through particular applications in quantum information science and each competing for being recognized as the most relevant measure of quantumness. In…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
Dempster-Shafer theory of evidence (D-S theory) is widely used in uncertain information process. The basic probability assignment(BPA) is a key element in D-S theory. How to measure the distance between two BPAs is an open issue. In this…
A finite-support constraint on the parameter space is used to derive a lower bound on the error of an estimator of the correlation coefficient in the bivariate exponential distribution. The bound is then exploited to examine optimality of…
This paper examines the relationship between Shafer's belief functions and convex sets of probability distributions. Kyburg's (1986) result showed that belief function models form a subset of the class of closed convex probability…
The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its…
Both the Bayes factor and the relative belief ratio satisfy the principle of evidence and so can be seen to be valid measures of statistical evidence. Certainly Bayes factors are regularly employed. The question then is: which of these…
This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical…
A quantitative measure of quantum coherence was recently introduced, in the context of quantum information theory. This measure has also been propounded as a good quantifier of the wave nature of quantum objects. However, actually measuring…
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…
Quantum discord as a measure of the quantum correlations cannot be easily computed for most of density operators. In this paper, we present a measure of the total quantum correlations that is operationally simple and can be computed…
There are at least two ways to interpret numerical degrees of belief in terms of betting: (1) you can offer to bet at the odds defined by the degrees of belief, or (2) you can judge that a strategy for taking advantage of such betting…
Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities---this is the conjunction fallacy. One of the most discussed accounts of this…
Quantum coherence has wide-ranging applications from quantum thermodynamics to quantum metrology, quantum channel discrimination and even quantum biology. Thus, detecting and quantifying coherence are two fundamental problems in quantum…
When the performance of a team of agents exceeds our expectations or fall short of them, we often explain this by saying that there was some synergy in the team---either positive (the team exceeded our expectations) or negative (they fell…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable.…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…