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In empirical research, when we have multiple estimators for the same parameter of interest, a central question arises: how do we combine unbiased but less precise estimators with biased but more precise ones to improve the inference? Under…

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

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…

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and…

This paper introduces a first implementation of a novel likelihood-ratio-based approach for constructing confidence intervals for neural networks. Our method, called DeepLR, offers several qualitative advantages: most notably, the ability…

We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…

We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-\beta^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha^{'}. We show that this definition…

We consider the power to reject false values of the parameter in Frequentist methods for the calculation of confidence intervals. We connect the power with the physical significance (reliability) of confidence intervals for a parameter…

Different ways of extracting parameters of interest from combined data sets of separate experiments are investigated accounting for the systematic errors. It is shown, that the frequentist approach may yield larger $\chi^2$ values when…

Accurate quantification of model uncertainty has long been recognized as a fundamental requirement for trusted AI. In regression tasks, uncertainty is typically quantified using prediction intervals calibrated to a specific operating point,…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and…

The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…

Recent statistical evaluations for High-Energy Physics measurements, in particular those at the Large Hadron Collider, require careful evaluation of many sources of systematic uncertainties at the same time. While the fundamental aspects of…

We consider the goal of predicting how complex networks respond to chronic (press) perturbations when characterizations of their network topology and interaction strengths are associated with uncertainty. Our primary result is the…

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…

It is commonly required to detect change points in sequences of random variables. In the most difficult setting of this problem, change detection must be performed sequentially with new observations being constantly received over time.…

Confidence intervals are an established means of portraying uncertainty about an inferred parameter and can be generated through the use of confidence distributions. For a confidence distribution to be ideal, it must maintain frequentist…

The problem of incorporating information from observations received serially in time is widespread in the field of uncertainty quantification. Within a probabilistic framework, such problems can be addressed using standard filtering…

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…