Related papers: From Univariate to Multivariate Uncertainty Calcul…

We present batching as an omnibus device for uncertainty quantification using simulation output. We consider the classical context of a simulationist performing uncertainty quantification on an estimator $\theta_n$ (of an unknown fixed…

The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…

Many uncertainty propagation software exist, written in different programming languages, but not all of them are able to handle functional correlation between quantities. In this paper we review one strategy to deal with uncertainty…

The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…

We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk…

Virtual experiments (VEs), a modern tool in metrology, can be used to help perform an uncertainty evaluation for the measurand. Current guidelines in metrology do not cover the many possibilities to incorporate VEs into an uncertainty…

Reliable uncertainty quantification is essential for the use of machine learning in physics, where scientific discoveries depend on validated probabilistic statements. We provide a structured overview of uncertainty quantification in ML for…

Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…

Quantiles are a fundamental concept in probability and theoretical statistics and a daily tool in their applications. While the univariate concept of quantiles is quite clear and well understood, its multivariate extension is more…

Uncertainty in machine learning is not generally taught as general knowledge in Machine Learning course curricula. In this paper we propose a short curriculum for a course about uncertainty in machine learning, and complement the course…

The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…

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…

Uncertainty quantification approaches have been more critical in large language models (LLMs), particularly high-risk applications requiring reliable outputs. However, traditional methods for uncertainty quantification, such as…

The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…

Estimating uncertainty of machine learning models is essential to assess the quality of the predictions that these models provide. However, there are several factors that influence the quality of uncertainty estimates, one of which is the…

Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…

This paper introduces a new approach to quantify the impact of forward propagated demand and weather uncertainty on power system planning and operation models. Recent studies indicate that such sampling uncertainty, originating from demand…

In the context of industrially mass-manufactured products, quality management is based on physically inspecting a small sample from a large batch and reasoning about the batch's quality conformance. When complementing physical inspections…

We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…

Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…