相关论文: A total uncertainty measure for D numbers based on…

The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…

Deep neural networks (DNNs) have received tremendous attention and achieved great success in various applications, such as image and video analysis, natural language processing, recommendation systems, and drug discovery. However, inherent…

Specially customised Entropies are widely applied in measuring the degree of uncertainties existing in the frame of discernment. However, all of these entropies regard the frame as a whole that has already been determined which dose not…

The problem of quantifying uncertainty about the locations of multiple change points by means of confidence intervals is addressed. The asymptotic distribution of the change point estimators obtained as the local maximisers of moving sum…

Uncertainty estimation bears the potential to make deep learning (DL) systems more reliable. Standard techniques for uncertainty estimation, however, come along with specific combinations of strengths and weaknesses, e.g., with respect to…

When ignorance due to the lack of knowledge, modeled as epistemic uncertainty using Dempster-Shafer structures on closed intervals, is present in the model parameters, a new uncertainty propagation method is necessary to propagate both…

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…

Deep learning has achieved impressive performance on many tasks in recent years. However, it has been found that it is still not enough for deep neural networks to provide only point estimates. For high-risk tasks, we need to assess the…

Measurement theory is the cornerstone of science, but no equivalent theory underpins the huge volumes of non-numerical data now being generated. In this study, we show that replacing numbers with alternative mathematical models, such as…

The problem of combining beliefs in the Dempster-Shafer belief theory has attracted considerable attention over the last two decades. The classical Dempster's Rule has often been criticised, and many alternative rules for belief combination…

We propose nonparametric estimation of divergence measures between continuous distributions. Our approach is based on a plug-in kernel- type estimators of density functions. We give the uniform in bandwidth consistency for the proposal…

We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…

General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…

We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the…

Common statistical measures of uncertainty such as $p$-values and confidence intervals quantify the uncertainty due to sampling, that is, the uncertainty due to not observing the full population. However, sampling is not the only source of…

The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…

The Dempster--Shafer (DS) theory is a powerful tool for probabilistic reasoning based on a formal calculus for combining evidence. DS theory has been widely used in computer science and engineering applications, but has yet to reach the…

A rise in popularity of Deep Neural Networks (DNNs), attributed to more powerful GPUs and widely available datasets, has seen them being increasingly used within safety-critical domains. One such domain, self-driving, has benefited from…

It is pointed out that the case for Shannon entropy and von Neumann entropy, as measures of uncertainty in quantum mechanics, is not as bleak as suggested in quant-ph/0006087. The main argument of the latter is based on one particular…

Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty…