Related papers: Robust Confidence Bands for Stochastic Processes U…

Inference via simultaneous confidence band is studied for stationary covariance function of dense functional data. A two-stage estimation procedure is proposed based on spline approximation, the first stage involving estimation of all the…

This article concerns the application of bootstrap methodology to construct a likelihood-based confidence region for operating conditions associated with the maximum of a response surface constrained to a specified region. Unlike classical…

The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making…

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…

Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…

We provide finite-sample performance guarantees for control policies executed on stochastic robotic systems. Given an open- or closed-loop policy and a finite set of trajectory rollouts under the policy, we bound the expected value,…

Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…

Simulation-based falsification is a practical testing method to increase confidence that the system will meet safety requirements. Because full-fidelity simulations can be computationally demanding, we investigate the use of simulators with…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

Motivated by critical challenges and needs from biopharmaceuticals manufacturing, we propose a general metamodel-assisted stochastic simulation uncertainty analysis framework to accelerate the development of a simulation model with modular…

We consider the problem of deciding on sampling strategy, in particular sampling design. We propose a risk measure, whose minimizing value guides the choice. The method makes use of a superpopulation model and takes into account uncertainty…

Semantic segmentation networks (SSNs) are central to safety-critical applications such as medical imaging and autonomous driving, where robustness under uncertainty is essential. However, existing probabilistic verification methods often…

When we use simulation to evaluate the performance of a stochastic system, the simulation often contains input distributions estimated from real-world data; therefore, there is both simulation and input uncertainty in the performance…

The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson--Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Two methods of…

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…

The classical single-band uncertainty model introduced by Bertsimas and Sim has represented a breakthrough in the development of tractable robust counterparts of Linear Programs. However, adopting a single deviation band may be too…

Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…

As the complexity of control systems increases, the need for systematic methods to guarantee their efficacy grows as well. However, direct testing of these systems is oftentimes costly, difficult, or impractical. As a result, the test and…

Our goal is to compute a policy that guarantees improved return over a baseline policy even when the available MDP model is inaccurate. The inaccurate model may be constructed, for example, by system identification techniques when the true…

Robust optimization methods have shown practical advantages in a wide range of decision-making applications under uncertainty. Recently, their efficacy has been extended to multi-period settings. Current approaches model uncertainty either…