Related papers: A Theory of Measurement Uncertainty Based on Condi…
We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define…
Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…
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…
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…
In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…
I explore the use of sets of probability measures as a representation of uncertainty.
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…
Quantitative characterizations and estimations of uncertainty are of fundamental importance in optimization and decision-making processes. Herein, we propose intuitive scores, which we call certainty and doubt, that can be used in both a…
Bayesian inference is used to estimate continuous parameter values given measured data in many fields of science. The method relies on conditional probability densities to describe information about both data and parameters, yet the notion…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
Although there are many mathematical theories to address uncertain phenomena however, these theories are presented under implicit presupposition that uncertainty of objects is accurately measurable while not considering that the measure of…
Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
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…
Concerning systematic effects, the recommendation given in the GUM is to correct for them, but unfortunately no detailed information is available, how to do this. This publication will show, how systematic measurement deviations can be…
Although a system is described by a well-known set of equations leading to a deterministic behavior, in the real world the value of a measurand obtained by an experiment will mostly scatter. Accordingly, an uncertainty is associated with…