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We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk…

This paper addresses the classical problem of determining the set of possible states of a linear discrete-time system subject to bounded disturbances from measurements corrupted by bounded noise. These so-called uncertainty sets evolve with…

RooStats is a project to create advanced statistical tools required for the analysis of LHC data, with emphasis on discoveries, confidence intervals, and combined measurements. The idea is to provide the major statistical techniques as a…

As large language models (LLMs) continue to evolve, understanding and quantifying the uncertainty in their predictions is critical for enhancing application credibility. However, the existing literature relevant to LLM uncertainty…

Frailty models are often the model of choice for heterogeneous survival data. A frailty model contains both random effects and fixed effects, with the random effects accommodating for the correlation in the data. Different estimation…

We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions…

Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…

A comprehensive uncertainty estimation is vital for the precision program of the LHC. While experimental uncertainties are often described by stochastic processes and well-defined nuisance parameters, theoretical uncertainties lack such a…

One way to incorporate systematic uncertainties into the calculation of confidence intervals is by integrating over probability density functions parametrizing the uncertainties. In this note we present a development of this method which…

Unbinned maximum likelihood is a common procedure for parameter estimation. After parameters have been estimated, it is crucial to know whether the fit model adequately describes the experimental data. Univariate Goodness of Fit procedures…

Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data…

Roughness parameters that characterize contacting surfaces with regard to friction and wear are commonly stated without uncertainties, or with an uncertainty only taking into account a very limited amount of aspects such as repeatability of…

Large Language Models (LLMs) excel in text generation, reasoning, and decision-making, enabling their adoption in high-stakes domains such as healthcare, law, and transportation. However, their reliability is a major concern, as they often…

In this work, we investigate Batch Normalization technique and propose its probabilistic interpretation. We propose a probabilistic model and show that Batch Normalization maximazes the lower bound of its marginalized log-likelihood. Then,…

Reliable uncertainty quantification is essential for the use of machine learning in physics, where scientific discoveries depend on validated probabilistic statements. We provide a structured overview of uncertainty quantification in ML for…

Systematic uncertainties in high energy physics and astrophysics are often significant contributions to the overall uncertainty in a measurement, in many cases being comparable to the statistical uncertainties. However, consistent…

We address the problem of uncertainty quantification for graph-structured data, or, more specifically, the problem to quantify the predictive uncertainty in (semi-supervised) node classification. Key questions in this regard concern the…

Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…

We show how to deal with uncertainties on the Standard Model predictions in an agnostic new physics search strategy that exploits artificial neural networks. Our approach builds directly on the specific Maximum Likelihood ratio treatment of…

Traditional approaches to ensure group fairness in algorithmic decision making aim to equalize ``total'' error rates for different subgroups in the population. In contrast, we argue that the fairness approaches should instead focus only on…