In this paper we demonstrate the only available scalable information bounds for quantities of interest of high dimensional probabilistic models. Scalability of inequalities allows us to (a) obtain uncertainty quantification bounds for quantities of interest in the large degree of freedom limit and/or at long time regimes; (b) assess the impact of large model perturbations as in nonlinear respon...

Uncertainty theory is a branch of mathematics that deals with human uncertainty, and uncertain variable is used to model an uncertain quantity. Uncertainty exists not only in real quantities but also in complex quantities. Complex uncertain variable is mainly used to model a complex uncertain quantity. In uncertainty theory, inverse uncertainty distribution provides an easy way to calculate exp...

The estimation of remaining useful life is significant in the context of prognostics and health monitoring, and the prediction of remaining useful life is essential for online operations and decision-making. However, it is challenging to accurately predict the remaining useful life in practical aerospace applications due to the presence of various uncertainties that affect prognostic calculatio...

Consider approximating a “black box” function f by an emulator f̂ based on n noiseless observations of f . Let w be a point in the domain of f . How big might the error |f̂(w) − f(w)| be? If f could be arbitrarily rough, this error could be arbitrarily large: we need some constraint on f besides the data. Suppose f is Lipschitz with a known constant. We find a lower bound on the number of observa...

Metas.UncLib is a software library that facilitates the linear propagation of uncertainties through a measurement model. It is able to handle complex-valued and multivariate quantities and supports higher mathematics. It is therefore able to deal with advanced metrological problems that require, e.g., matrix manipulations. The software is optimized for short computation times and low memory use...

We consider the question of entropic uncertainty relations for prime power dimensions. In order to improve upon such uncertainty relations for higher dimensional quantum systems, we derive a tight lower bound amount of entropy for multiple probability distributions under the constraint that the sum of the collision probabilities for all distributions is fixed. This is purely a classical informa...