Related papers: Analyzing Uncertainty Matrices Associated with Mul…

Uncertainty lower bounds for parameter estimations associated with a unitary family of mixed-state density matrices are obtained by embedding the space of density matrices in the Hilbert space of square-root density matrices. In the…

Deep learning has the potential to dramatically impact navigation and tracking state estimation problems critical to autonomous vehicles and robotics. Measurement uncertainties in state estimation systems based on Kalman and other Bayes…

Classifiers are often tested on relatively small data sets, which should lead to uncertain performance metrics. Nevertheless, these metrics are usually taken at face value. We present an approach to quantify the uncertainty of…

Roughness parameters that characterize contacting surfaces with regard to friction and wear are commonly stated without uncertainties, or with an uncertainty only taking into account a very limited amount of aspects such as repeatability of…

Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…

Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over…

In this paper we analyze a recent experiment conducted in an anechoic chamber, where the scattering of microwaves from an array of metallic cylinders was measured. This is a system which displays chaotic scattering in the short wave limit.…

Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…

A technique for characterizing and correcting the linearity of radiometric instruments is known by the names the "flux-addition method" and the "combinatorial technique". In this paper, we develop a rigorous uncertainty quantification…

Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we…

We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this result to derive the variance-covariance matrix of the sample…

Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating…

We study two spiked models of random matrices under general frameworks corresponding respectively to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the…

This paper is concerned with the channel estimation problem in millimetre wave (MMW) wireless systems with large antenna arrays. By exploiting the sparse nature of the MMW channel, we present an efficient estimation algorithm based on a…

For many applications it is critical to know the uncertainty of a neural network's predictions. While a variety of neural network parameter estimation methods have been proposed for uncertainty estimation, they have not been rigorously…

Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…

Neural Networks have high accuracy in solving problems where it is difficult to detect patterns or create a logical model. However, these algorithms sometimes return wrong solutions, which become problematic in high-risk domains like…

This chapter reviews methods for linear shrinkage of the sample covariance matrix (SCM) and matrices (SCM-s) under elliptical distributions in single and multiple populations settings, respectively. In the single sample setting a popular…

Modern autonomous systems with machine learning components often use uncertainty quantification to help produce assurances about system operation. However, there is a lack of consensus in the community on what uncertainty is and how to…