Related papers: Model uncertainty and reference value of the Planc…
In this work, the uncertainties in the dielectric constants of polar liquids, computed using molecular dynamics (MD) simulations, are compared for two different calculations schemes. Expressions of the uncertainty are derived for the…
Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…
We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate…
We report a new measurement of the ratio $h/m_{\mathrm{Rb}}$ between the Planck constant and the mass of $^{87}\mathrm{Rb}$ atom. A new value of the fine structure constant is deduced, $\alpha^{-1}=137.035\,999\,037\,(91)$ with a relative…
The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…
Accurately estimating uncertainties in neural network predictions is of great importance in building trusted DNNs-based models, and there is an increasing interest in providing accurate uncertainty estimation on many tasks, such as security…
Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps.…
We present a method to quantify uncertainty in the predictions made by simulations of mathematical models that can be applied to a broad class of stochastic, discrete, and differential equation models. Quantifying uncertainty is crucial for…
The uncertainty principle is considered to be one of the most striking features in quantum mechanics. In the textbook literature, uncertainty relations usually refer to the preparation uncertainty which imposes a limitation on the spread of…
A discussion is given of the uncertainty principle in view of the introduction of a Gravitational Planck Constant. The need for such a gravitational constant is shown first. A reduced electromagnetic Planck constant and the analogous…
Existing approaches to model uncertainty typically either compare models using a quantitative model selection criterion or evaluate posterior model probabilities having set a prior. In this paper, we propose an alternative strategy which…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
Stated choice probabilities are increasingly used in conjunction with the random-coefficient model (RCM) to describe individual preferences. They allow survey respondents to express uncertainty about the future or the incompleteness of a…
Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…
A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
Theoretical predictions need quantified uncertainties for a meaningful comparison to experimental results. This is an idea which presently permeates the field of theoretical nuclear physics. In light of the recent progress in estimating…