Related papers: A new combination approach based on improved evide…
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…
Dempster-Shafer structure is effective in classical settings for connecting set-valued hypotheses and representing structured ignorance, yet its practical use is limited by combination growth over focal sets and high conflict management. We…
It is known that humans can easily read words where the letters have been jumbled in a certain way. This paper examines this problem by associating a distance measure with the jumbling process. Modifications to text were generated according…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
Gilbert proposed an algorithm for bounding the distance between a given point and a convex set. In this article we apply the Gilbert's algorithm to get an upper bound on the Hilbert-Schmidt distance between a given state and the set of…
Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling…
A control strategy for expert systems is presented which is based on Shafer's Belief theory and the combination rule of Dempster. In contrast to well known strategies it is not sequentially and hypotheses-driven, but parallel and self…
In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…
Modifiable combining functions are a synthesis of two common approaches to combining evidence. They offer many of the advantages of these approaches and avoid some disadvantages. Because they facilitate the acquisition, representation,…
Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual…
We present a Dempster--Shafer (DS) approach to estimating limits from Poisson counting data with nuisance parameters. Dempster--Shafer is a statistical framework that generalizes Bayesian statistics. DS calculus augments traditional…
In various data settings, it is necessary to compare observations from disparate data sources. We assume the data is in the dissimilarity representation and investigate a joint embedding method that results in a commensurate representation…
The Wasserstein distance between mixing measures has come to occupy a central place in the statistical analysis of mixture models. This work proposes a new canonical interpretation of this distance and provides tools to perform inference on…
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…
This paper develops new methodology, together with related theories, for combining information from independent studies through confidence distributions. A formal definition of a confidence distribution and its asymptotic counterpart (i.e.,…
Consider a finite directed graph without cycles in which the arrows are weighted. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context…
Fusing and sharing information from multiple sensors over a network is a challenging task, partly due to the absence of a foundational rule for fusing probability distributions that preserves the independence of sources. To address this, we…
This paper develops a mathematical and computational framework for analyzing the expected performance of Bayesian data fusion, or joint statistical inference, within a sensor network. We use variational techniques to obtain the posterior…