Related papers: Contradiction measures and specificity degrees of …
The aim of this article is to make a contribution to the Bayesian procedure of testing precise hypotheses for parametric models. For this purpose, we define the Bayesian Discrepancy Measure that allows one to evaluate the suitability of a…
We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…
By analyzing the relationships among chance, weight of evidence and degree of beliefwe show that the assertion "probability functions are special cases of belief functions" and the assertion "Dempster's rule can be used to combine belief…
Measures of discordance between datasets have become an essential part of cosmological analyses. It is important to accurately evaluate the significance of such discordances when present. We propose here a Bayesian interpretation of…
Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
The theory of belief functions manages uncertainty and also proposes a set of combination rules to aggregate opinions of several sources. Some combination rules mix evidential information where sources are independent; other rules are…
Interpreting experimental data in high school experiments can be a difficult task for students, especially when there is large variation in the data. At the same time, calculating the standard deviation poses a challenge for students. In…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
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…
Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate…
How should we quantify the inconsistency of a database that violates integrity constraints? Proper measures are important for various tasks, such as progress indication and action prioritization in cleaning systems, and reliability…
We examine a family of intrinsic performance measures in terms of probability distributions that generalize Hellinger distance and Fisher information. They are applied to quantum metrology to assess the uncertainty in the detection of…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
The investigation of uncertainty is of major importance in risk-critical applications, such as medical image segmentation. Belief function theory, a formal framework for uncertainty analysis and multiple evidence fusion, has made…
Consistent belief functions represent collections of coherent or non-contradictory pieces of evidence, but most of all they are the counterparts of consistent knowledge bases in belief calculus. The use of consistent transformations cs[.]…
As a generalization of Dempster-Shafer theory, the theory of D numbers is a new theoretical framework for uncertainty reasoning. Measuring the uncertainty of knowledge or information represented by D numbers is an unsolved issue in that…