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In this note we consider coverage of confidence intervals calculated with and without systematic uncertainties. These calculations follow the prescription originally proposed by Cousins & Highland but here extended to account for different…

We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…

In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a…

In Neyman's original formulation, a 1-alpha confidence interval procedure is justified by its long-run coverage properties, and a single realized interval is to be described only by the slogan that it either covers the parameter or it does…

Classically, confidence intervals are required to have consistent coverage across all values of the parameter. However, this will inevitably break down if the underlying estimation procedure is biased. For this reason, many efforts have…

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We…

We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (2013). In particular the candidate models used can…

We develop a method to generate prediction sets with a guaranteed coverage rate that is robust to corruptions in the training data, such as missing or noisy variables. Our approach builds on conformal prediction, a powerful framework to…

Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…

For any class of one-sided $1-\alpha$ confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two…

We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a…

In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…

In this manuscript we review two methods to construct exact confidence bounds for an unknown real parameter in a general class of discrete statistical models. These models include the binomial family, the Poisson family as well as…

Expected coverage and expected length of 90% upper and lower limit and 68.27% central intervals are plotted as functions of the true signal for various values of expected background. Results for several objective priors are shown, and…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…

An important factor to guarantee a fair use of data-driven recommendation systems is that we should be able to communicate their uncertainty to decision makers. This can be accomplished by constructing prediction intervals, which provide an…

The current standard for confidence interval construction in the context of a possibly misspecified model is to use an interval based on the sandwich estimate of variance. These intervals provide asymptotically correct coverage, but…

This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…

Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…