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Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional…

Optimization and Control · Mathematics 2020-01-06 Joseph Hart , Bart van Bloemen Waanders , Roland Herzog

Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…

Physics and Society · Physics 2018-05-15 Filippo Radicchi , Claudio Castellano

For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…

Statistics Theory · Mathematics 2022-02-17 Jack Noonan , Anatoly Zhigljavsky

Uncertainty estimation bears the potential to make deep learning (DL) systems more reliable. Standard techniques for uncertainty estimation, however, come along with specific combinations of strengths and weaknesses, e.g., with respect to…

Machine Learning · Computer Science 2022-05-02 Joachim Sicking , Maram Akila , Jan David Schneider , Fabian Hüger , Peter Schlicht , Tim Wirtz , Stefan Wrobel

We consider clinical trials in which an experimental treatment is compared with a control in pre-specified patient subpopulations. In such settings, adaptive enrichment designs allow the enrolled population to be modified at an interim…

Methodology · Statistics 2026-03-17 Enyu Li , Nigel Stallard , Ekkehard Glimm , Dominic Magirr , Peter K. Kimani

This paper introduces a practical sampling method for training surrogate models in the context of uncertainty propagation. We propose a heuristic method to uniformly draw samples within highest density regions of the density given by the…

Methodology · Statistics 2025-09-15 Jocelyn Minini , Micha Wasem

This paper concerns robust inference on average treatment effects following model selection. In the selection on observables framework, we show how to construct confidence intervals based on a doubly-robust estimator that are robust to…

Statistics Theory · Mathematics 2018-04-13 Max H. Farrell

Hierarchical random effect models are used for different purposes in clinical research and other areas. In general, the main focus is on population parameters related to the expected treatment effects or group differences among all units of…

Applications · Statistics 2021-04-07 Maryna Prus , Norbert Benda , Rainer Schwabe

Controlled experiments are widely used in many applications to investigate the causal relationship between input factors and experimental outcomes. A completely randomized design is usually used to randomly assign treatment levels to…

Methodology · Statistics 2026-05-12 Yiou Li , Lulu Kang , Xiao Huang

Fitting models to data is an important part of the practice of science. Advances in machine learning have made it possible to fit more -- and more complex -- models, but have also exacerbated a problem: when multiple models fit the data…

Methodology · Statistics 2025-10-27 Alexandre René , André Longtin

This paper studies the use of highly stratified designs for the efficient estimation of a large class of treatment effect parameters that arise in the analysis of experiments. By a "highly stratified" design, we mean experiments in which…

Econometrics · Economics 2026-03-30 Yuehao Bai , Jizhou Liu , Azeem M. Shaikh , Max Tabord-Meehan

Optimizing the design of complex systems requires navigating interdependent decisions, heterogeneous components, and multiple objectives. Our monotone theory of co-design offers a compositional framework for addressing this challenge,…

Systems and Control · Electrical Eng. & Systems 2025-08-13 Yujun Huang , Marius Furter , Gioele Zardini

Both the level of conservativeness and the computational burden in robust optimization are critically influenced by uncertainty set design. However, contextual side information is rarely exploited in robust dispatch of power systems…

Optimization and Control · Mathematics 2026-05-11 Zhaojun Ruan , Yulin Liu , Le Fu , Libao Shi

In this review, we present econometric and statistical methods for analyzing randomized experiments. For basic experiments we stress randomization-based inference as opposed to sampling-based inference. In randomization-based inference,…

Methodology · Statistics 2017-10-26 Susan Athey , Guido Imbens

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…

High Energy Physics - Phenomenology · Physics 2023-05-08 Aishik Ghosh , Benjamin Nachman , Tilman Plehn , Lily Shire , Tim M. P. Tait , Daniel Whiteson

This article studies the benefits of using spatially randomized experimental designs which partition the experimental area into distinct, non-overlapping units with treatments assigned randomly. Such designs offer improved policy evaluation…

Statistics Theory · Mathematics 2025-11-18 Ying Yang , Chengchun Shi , Fang Yao , Shouyang Wang , Hongtu Zhu

Trust is a crucial factor affecting the adoption of machine learning (ML) models. Qualitative studies have revealed that end-users, particularly in the medical domain, need models that can express their uncertainty in decision-making…

Machine Learning · Computer Science 2023-04-21 Andrew Houston , Georgina Cosma

Empiric antibiotic prescribing in high-risk clinical contexts often requires decision making under conditions of incomplete information, where inappropriate coverage or unjustified escalation may compromise safety and antimicrobial…

Computers and Society · Computer Science 2026-03-12 Francisco José Gárate , Paloma Chausa , Diego Moreno , Judit López Luque , Vicens Díaz-Brito , Enrique Javier Gómez

Many applications of machine learning methods involve an iterative protocol in which data are collected, a model is trained, and then outputs of that model are used to choose what data to consider next. For example, one data-driven approach…

Machine Learning · Computer Science 2025-04-07 Clara Fannjiang , Stephen Bates , Anastasios N. Angelopoulos , Jennifer Listgarten , Michael I. Jordan

Typically, a randomized experiment is designed to test a hypothesis about the average treatment effect and sometimes hypotheses about treatment effect variation. The results of such a study may then be used to inform policy and practice for…

Methodology · Statistics 2026-05-01 Elizabeth Tipton , Michalis Mamakos