Related papers: Contradiction measures and specificity degrees of …
We study quantum measurement retrodiction using the principle of minimum change. For quantum-to-classical measurement channels, we show that all standard quantum divergences select the same retrodictive update, yielding a unique and…
Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. In this paper, we put forward a quantitative measure of coherence by following the axiomatic definition of coherence measures introduced…
This paper presents some ideas and results of using uncertainty management methods in the presence of data in preference to other statistical and machine learning methods. A medical domain is used as a test-bed with data available from a…
Impossibility results show that important fairness measures (independence, separation, sufficiency) cannot be satisfied at the same time under reasonable assumptions. This paper explores whether we can satisfy and/or improve these fairness…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by…
The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in…
As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty…
Prediction of future observations is an important and challenging problem. The two mainstream approaches for quantifying prediction uncertainty use prediction regions and predictive distributions, respectively, with the latter believed to…
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we…
Most questionnaires offer ordered responses whose order is poorly studied via belief functions. In this paper, we study the consequences of a frame of discernment consisting of ordered elements on belief functions. This leads us to redefine…
This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…
There is available an ever-increasing variety of procedures for managing uncertainty. These methods are discussed in the literature of artificial intelligence, as well as in the literature of philosophy of science. Heretofore these methods…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set,…
In this paper we investigate the question of how much combined measurements can increase the accuracy of additive quantities. Therefore, we consider a set of measurements from a selection of all possible combinations of the $n$ labeled…
With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…
Facing an unknown situation, a person may not be able to firmly elicit his/her preferences over different alternatives, so he/she tends to express uncertain preferences. Given a community of different persons expressing their preferences…
Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A…
Macroscopic behavior such as the lack of interference patterns has been attributed to "decoherence", a word with several possible definitions such as (1) the loss of off-diagonal density matrix elements, (2) the flow of information to the…