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Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…

Probability Quantification (PQ) predictions of the efficacy of safety-critical protective systems is challenging. Yet, the popularity of PQ methodologies (e.g., Probabilistic Risk Assessment (PRA), Quantitative Risk Analysis (QRA) and…

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…

In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the…

The comprehensive integration of machine learning healthcare models within clinical practice remains suboptimal, notwithstanding the proliferation of high-performing solutions reported in the literature. A predominant factor hindering…

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…

Simulations using machine learning (ML) models and mechanistic models are often run to inform decision-making processes. Uncertainty estimates of simulation results are critical to the decision-making process because simulation results of…

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. Most of these models involve inherent uncertainties that must be assessed to increase the confidence in model predictions…

Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this…

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…

Prediction uncertainty estimation has clinical significance as it can potentially quantify prediction reliability. Clinicians may trust 'blackbox' models more if robust reliability information is available, which may lead to more models…

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…

Given an imprecise probabilistic model over a continuous space, computing lower/upper expectations is often computationally hard to achieve, even in simple cases. Because expectations are essential in decision making and risk analysis,…

The probabilistic cellular automaton (PCA) method is highlighted for its relatively simple numerical algorithm and low computational cost in the simulation of microstructural evolution. In this method, probabilistic state change rules are…

Constructing flexible probability models that respect constraints on key functionals -- such as the mean -- is a fundamental problem in nonparametric statistics. Existing approaches lack systematic tools for enforcing such constraints while…

The radiological characterization of contaminated elements (walls, grounds, objects) from nuclear facilities often suffers from a too small number of measurements. In order to determine risk prediction bounds on the level of contamination,…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

Uncertainty estimation, which provides a means of building explainable neural networks for medical imaging applications, have mostly been studied for single deep learning models that focus on a specific task. In this paper, we propose a…