Related papers: Computing conservative probabilities of rare event…
Explicitly accounting for uncertainties is paramount to the safety of engineering structures. Optimization which is often carried out at the early stage of the structural design offers an ideal framework for this task. When the…
Properly estimating correlations between objects at different spatial scales necessitates $\mathcal{O}(n^2)$ distance calculations. For this reason, most widely adopted packages for estimating correlations use clustering algorithms to…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by…
Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are…
The ongoing development of quantum processors is driving breakthroughs in scientific discovery. Despite this progress, the formidable cost of fabricating large-scale quantum processors means they will remain rare for the foreseeable future,…
This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form…
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…
Though the ability of human beings to deal with probabilities has been put into question, the assessment of rarity is a crucial competence underlying much of human decision-making and is pervasive in spontaneous narrative behaviour. This…
Optimization models used to make discrete decisions often contain uncertain parameters that are context-dependent and estimated through prediction. To account for the quality of the decision made based on the prediction, decision-focused…
Our work was motivated by a recent study on birth defects of infants born to pregnant women exposed to a certain medication for treating chronic diseases. Outcomes such as birth defects are rare events in the general population, which often…
The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an…
An unsupervised and a supervised classification approaches for Hilbert random curves are studied. Both rest on the use of a surrogate of the probability density which is defined, in a distribution-free mixture context, from an asymptotic…
When providing probabilistic forecasts for uncertain future events, it is common to strive for calibrated forecasts, that is, the predictive distribution should be compatible with the observed outcomes. Several notions of calibration are…
Failure probability evaluation for complex physical and engineering systems governed by partial differential equations (PDEs) are computationally intensive, especially when high-dimensional random parameters are involved. Since standard…
Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on…
Before we apply nonlinear techniques, for example those inspired by chaos theory, to dynamical phenomena occurring in nature, it is necessary to first ask if the use of such advanced techniques is justified "by the data". While many…
Surrogate endpoints are used in place of long-term outcomes in randomized experiments when observing the real outcome for a large enough cohort is prohibitively expensive or impractical. A short-term surrogate is good if the result of an…
Evaluating rare-event forecasts is challenging because standard metrics collapse as event prevalence declines. Measures such as F1-score, AUPRC, MCC, and accuracy induce degenerate thresholds -- converging to zero or one -- and their values…
We consider the problem of low probability estimation: given a machine learning model and a formally-specified input distribution, how can we estimate the probability of a binary property of the model's output, even when that probability is…