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Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. Closed-form expression of the sum distribution is usually intractable and presents an open problem. A crude Monte…

Resilience has emerged as a crucial concept for evaluating structural performance under disasters because of its ability to extend beyond traditional risk assessments, accounting for a system's ability to minimize disruptions and maintain…

Uncertainty estimation is a key issue when considering the application of deep neural network methods in science and engineering. In this work, we introduce a novel algorithm that quantifies epistemic uncertainty via Monte Carlo sampling…

A posteriori error analysis is a technique to quantify the error in particular simulations of a numerical approximation method. In this article, we use such an approach to analyze how various error components propagate in certain moving…

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…

We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…

The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of…

Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…

Bayesian methods are critical for quantifying the behaviors of systems. They capture our uncertainty about a system's behavior using probability distributions and update this understanding as new information becomes available. Probabilistic…

The expected value of information (EVI) is the most powerful measure of sensitivity to uncertainty in a decision model: it measures the potential of information to improve the decision, and hence measures the expected value of outcome.…

Seismic data frequently exhibits missing traces, substantially affecting subsequent seismic processing and interpretation. Deep learning-based approaches have demonstrated significant advancements in reconstructing irregularly missing…

Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…

Landslides are a recurring, widespread hazard. Preparation and mitigation efforts can be aided by a high-quality, large-scale dataset that covers global at-risk areas. Such a dataset currently does not exist and is impossible to construct…

Machine learning-based seismic processing models are typically trained separately to perform specific seismic processing tasks (SPTs), and as a result, require plenty of training data. However, preparing training data sets is not trivial,…

This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded…

In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an…

Experimental robot optimization often requires evaluating each candidate policy for seconds to minutes. The chosen evaluation time influences optimization because of a speed-accuracy tradeoff: shorter evaluations enable faster iteration,…

Robotic systems, particularly in demanding environments like narrow corridors or disaster zones, often grapple with imperfect state estimation. Addressing this challenge requires a trajectory plan that not only navigates these restrictive…

This study presents a methodology to treat performance-based seismic design as an inverse engineering problem, where design parameters are directly derived to achieve specific performance objectives. By implementing explainable machine…

Simulation-based inference (SBI) is constantly in search of more expressive and efficient algorithms to accurately infer the parameters of complex simulation models. In line with this goal, we present consistency models for posterior…