Measuring Uncertainty for Interval Belief Structures and its Application for Analyzing Weather Forecasts

A. Bronevich; Spiridenkova N.

doi:10.1007/978-3-319-66830-7_25

Publications

?

Measuring Uncertainty for Interval Belief Structures and its Application for Analyzing Weather Forecasts

P. 273–285.

Bronevich A., Spiridenkova N.

While analyzing statistical data we face with a problem of modeling uncertainty. One among well justified models is based on belief structures that allow us to describe imprecision and conflict in information. We use this model for analyzing contradiction in weather forecasts. For this aim we build several measures of contradiction based on the introduced imprecision index and the disjunctive aggregation rule for interval belief structures. We use these characteristics for analyzing weather forecasts.

Keywords: interval belief structures inclusion indices Wasserstein metric measures of contradiction

In book

Advances in Fuzzy Logic and Technology 2017

Vol. 642. , Cham: Springer, 2018.

A study of distributionally robust mixed-integer programming with Wasserstein metric: on the value of incomplete data

Sergey S. Ketkov, European Journal of Operational Research 2024 Vol. 313 No. 2 P. 602–615

This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in ...

Added: October 31, 2023

Measures of conflict, basic axioms and their application to the clusterization of a body of evidence

Andrey G. Bronevich, Alexander E. Lepskiy, Fuzzy Sets and Systems 2022 Vol. 446 P. 277–300

There are several approaches for evaluating conflict within belief functions. In this paper, we develop one of them based on axioms and show its connections to the decomposition approach. We describe a class of conflict measures satisfying this system of axioms and show that measuring conflict can be realized through the clusterization of a body ...

Added: August 27, 2022

The contradiction between belief functions: Its description, measurement, and correction based on generalized credal sets

Bronevich A., Rozenberg I., International Journal of Approximate Reasoning 2019 Vol. 112 P. 119–139

In the paper, we formalize the notion of contradiction between belief functions: we argue that belief functions are not contradictory if they provide non-contradictory models for decision-making. To elaborate on this idea, we take the decision rule from imprecise probabilities and show that sources of information described by belief functions are not contradictory iff the ...

Added: September 25, 2019

Existence and consistency of Wasserstein barycenters

Loubes J., Le Gouic T., Probability Theory and Related Fields 2017 P. 901–917

Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random probabilities defined on a geodesic space (E, d). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of ...

Added: October 13, 2018

On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

Boissard E., Le Gouic T., Annales de l'institut Henri Poincare (B) Probability and Statistics 2014 P. 539–563

In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by finitely supported measures (the quantization problem). It is found that ...

Added: October 13, 2018

Distribution’s template estimate with Wasserstein metrics

Boissard E., Le Gouic T., Loubes J., Bernoulli: a journal of mathematical statistics and probability 2015 P. 740–759

In this paper, we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an estimation of the mean distribution. Moreover, when the distributions are a common measure warped by a ...

Added: October 13, 2018

The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

Bronevich A., Rozenberg I., , in: Belief Functions: Theory and Applications 5th International Conference, BELIEF 2018, Compiègne, France, September 17-21, 2018, ProceedingsVol. 11069.: Springer, 2018. P. 31–38.

The aim of this paper is to show that the Kantorovich problem, well known in models of economics and very intensively studied in probability theory in recent years, can be viewed as the basis of some constructions in the theory of belief functions. We demonstrate this by analyzing specialization relation for finitely defined belief functions ...

Added: October 8, 2018