Related papers: Uncertainty Bounds for Spectral Estimation
We employ uncertain parametric CTMCs with parametric transition rates and a prior on the parameter values. The prior encodes uncertainty about the actual transition rates, while the parameters allow dependencies between transition rates.…
In the analysis of elastic-scattering experimental data, optical-model parameters (usually, depths of real and imaginary potentials) are fitted and conclusions are drawn analyzing their variations at bombardment energies close to the…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
In the real world, one almost never knows the parameters of a thermodynamic process to infinite precision. Reflecting this, here we investigate how to extend stochastic thermodynamics to systems with uncertain parameters, including…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices…
We obtain an essential spectral gap for $n$-dimensional convex co-compact hyperbolic manifolds with the dimension $\delta$ of the limit set close to $(n-1)/2$. The size of the gap is expressed using the additive energy of stereographic…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
When you measure an observable, A, in Quantum Mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some non-commuting observable, B. The standard Uncertainty Relation puts a lower bound on…
Uncertainty quantification by ensemble learning is explored in terms of an application from computational optical form measurements. The application requires to solve a large-scale, nonlinear inverse problem. Ensemble learning is used to…
Uncertainty estimation is essential to make neural networks trustworthy in real-world applications. Extensive research efforts have been made to quantify and reduce predictive uncertainty. However, most existing works are designed for…
Recent empirical work in the field of 'weak measurements' has yielded novel ways of more directly accessing and exploring the quantum wavefunction. Measuring either position or momentum for a photon in a 'weak' manner yields a wide range of…
Data integration is a notoriously difficult and heuristic-driven process, especially when ground-truth data are not readily available. This paper presents a measure of uncertainty by providing maximal and minimal ranges of a query outcome…
Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…
Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…
The power spectrum of mass density fluctuations is estimated from the Mark III and the SFI catalogs of peculiar velocities by applying a maximum likelihood analysis, using parametric models for the power spectrum and for the errors.…