Related papers: Factorization of Dempster-Shafer Belief Functions …
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…
Dempster-Shafer theory is widely applied to uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. However, some conditions, such as exclusiveness hypothesis and completeness constraint, limit…
Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a high computational burden. A lot of work has been done to reduce the complexity of computations used in…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
Multiple testing is a fundamental problem in high-dimensional statistical inference. Although many methods have been proposed to control false discoveries, it is still a challenging task when the tests are correlated to each other. To…
We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…
We study the problem of independence and conditional independence tests between categorical covariates and a continuous response variable, which has an immediate application in genetics. Instead of estimating the conditional distribution of…
As a generalization of Dempster-Shafer theory, D number theory provides a framework to deal with uncertain information with non-exclusiveness and incompleteness. However, some basic concepts in D number theory are not well defined. In this…
Likelihood-based inference, central in modern particle physics data analysis requires the extensive evaluation of a likelihood function that depends on set of parameters defined by the statistical model under consideration. If an analytical…
Partial correlation coefficients are widely applied in the social sciences to evaluate the relationship between two variables after accounting for the influence of others. In this article, we present Bayes Factor Functions (BFFs) for…
When assessing a software-based system, the results of Bayesian statistical inference on operational testing data can provide strong support for software reliability claims. For inference, this data (i.e. software successes and failures) is…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
Evidential reasoning in expert systems has often used ad-hoc uncertainty calculi. Although it is generally accepted that probability theory provides a firm theoretical foundation, researchers have found some problems with its use as a…
Efficient modeling of uncertain information in real world is still an open issue. Dempster-Shafer evidence theory is one of the most commonly used methods. However, the Dempster-Shafer evidence theory has the assumption that the hypothesis…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
In this paper, we generalize the belief function on complex plane from another point of view. We first propose a new concept of complex mass function based on the complex number, called complex basic belief assignment, which is a…
We view the syntax-based approaches to default reasoning as a model-based diagnosis problem, where each source giving a piece of information is considered as a component. It is formalized in the ATMS framework (each source corresponds to an…
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…
One problem to solve in the context of information fusion, decision-making, and other artificial intelligence challenges is to compute justified beliefs based on evidence. In real-life examples, this evidence may be inconsistent,…