Related papers: A new approach for imprecise probabilities
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…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty -- due to incomplete knowledge -- requires…
The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
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…
Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define several notions of randomness associated with interval, rather than precise,…
Improving Importance Sampling estimators for rare event probabilities requires sharp approx- imations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the…
We introduce the concept of partial law invariance, generalizing the concepts of law invariance and probabilistic sophistication widely used in decision theory, as well as statistical and financial applications. This new concept is…
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…
In this paper, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…