Related papers: Parameter uncertainties in weighted unbinned maxim…

Achieving the ultimate precisions for multiple parameters simultaneously is an outstanding challenge in quantum physics, because the optimal measurements for incompatible parameters cannot be performed jointly due to the Heisenberg…

As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…

This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…

In this paper, we develop statistical inference techniques for the unknown coefficient functions and single-index parameters in single-index varying-coefficient models. We first estimate the nonparametric component via the local linear…

We consider the problem of setting confidence intervals on a parameter of interest from the maximum-likelihood fit of a physics model to a binned data set with a large number of bins, large event-counts per bin, and in the presence of…

Parameter estimation based on uncertain data represented as belief structures is one of the latest problems in the Dempster-Shafer theory. In this paper, a novel method is proposed for the parameter estimation in the case where belief…

We consider an empirical likelihood inference for parameters defined by general estimating equations when some components of the random observations are subject to missingness. As the nature of the estimating equations is wide-ranging, we…

We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for…

Recently, Halpern and Leung suggested representing uncertainty by a weighted set of probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not…

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…

This paper describes the treatment of systematic uncertainties in a Likelihood formalism. RooUnfold, which includes most of the unfolding methods that are commonly used in particle physics, is used to compare a newly implemented method…

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…

Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to…

Naive maximum likelihood estimation of binary logit models with fixed effects leads to unreliable inference due to the incidental parameter problem. We study the case of three-dimensional panel data, where the model includes three sets of…

The use of high-dimensional regression techniques from machine learning has significantly improved the quantitative accuracy of interatomic potentials. Atomic simulations can now plausibly target quantitative predictions in a variety of…

Photoplethysmography (PPG) signals encode information about relative changes in blood volume that can be used to assess various aspects of cardiac health non-invasively, e.g.\ to detect atrial fibrillation (AF) or predict blood pressure…

We derive new inequalities for the probabilities of projective measurements in mutually unbiased bases of a qudit system. These inequalities lead to wider ranges of validity and tighter bounds on entropic uncertainty inequalities previously…

Many common loss functions such as mean-squared-error, cross-entropy, and reconstruction loss are unnecessarily rigid. Under a probabilistic interpretation, these common losses correspond to distributions with fixed shapes and scales. We…

Parameter estimation and inference from complex survey samples typically focuses on global model parameters whose estimators have asymptotic properties, such as from fixed effects regression models. The central challenge is to both mitigate…

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…