Related papers: Error Estimates of Theoretical Models: a Guide

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…

Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of…

The uncertainty quantifications of theoretical results are of great importance to make meaningful comparisons of those results with experimental data and to make predictions in experimentally unknown regions. By quantifying uncertainties,…

We discuss the least-square and linear-regression methods, which are relevant for a reliable determination of good nuclear-mass-model parameter sets and their errors. In this perspective, we define exact and inaccurate models and point out…

This guide aims at providing a general introduction to bootstrap methods. By using simple examples taken from nuclear physics, I discuss how such a method can be used to quantify error bars of an estimator. I also investigate the use of…

Sources of uncertainty are reviewed for calculated atomic and molecular data that are important for plasma modeling: atomic and molecular structure and cross sections for electron-atom, electron-molecule, and heavy particle collisions. We…

Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate…

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…

ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…

Future neutrino-oscillation experiments are expected to bring definite answers to the questions of neutrino-mass hierarchy and violation of charge-parity symmetry in the lepton sector. To realize this ambitious program it is necessary to…

Ensemble models can be used to estimate prediction uncertainties in machine learning models. However, an ensemble of N models is approximately N times more computationally demanding compared to a single model when it is used for inference.…

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…

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…

Improving the accuracy of forecast models for physical systems such as the atmosphere is a crucial ongoing effort. Errors in state estimation for these often highly nonlinear systems has been the primary focus of recent research, but as…

Computational models in chemistry rely on a number of approximations. The effect of such approximations on observables derived from them is often unpredictable. Therefore, it is challenging to quantify the uncertainty of a computational…

The application of effective field theory (EFT) methods to nuclear systems provides the opportunity to rigorously estimate the uncertainties originating in the nuclear Hamiltonian. Yet this is just one source of uncertainty in the…

Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated…

Uncertainty quantification of complex technical systems is often based on a computer model of the system. As all models such a computer model is always wrong in the sense that it does not describe the reality perfectly. The purpose of this…

Theoretical predictions of physical observables often involve extrapolations to regions that are poorly constrained by laboratory experiments and astrophysical observations. Without properly quantified theoretical errors, such model…

Uncertainty quantification has emerged as a rapidly growing field in nuclear science. Theoretical predictions of physical observables often involve extrapolations to regions that are poorly constrained by laboratory experiments and…