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Conformal prediction is widely used to equip black-box machine learning models with uncertainty quantification, offering formal coverage guarantees under exchangeable data. However, these guarantees fail when faced with subpopulation…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated…
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
Approximate Bayesian Computation (ABC) is a popular computational method for likelihood-free Bayesian inference. The term "likelihood-free" refers to problems where the likelihood is intractable to compute or estimate directly, but where it…
This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…
A random neighbor extremal stick-slip model is introduced. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter, is exactly calculable. The…
When are asymptotic approximations using the delta-method uniformly valid? We provide sufficient conditions as well as closely related necessary conditions for uniform negligibility of the remainder of such approximations. These conditions…
This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…
Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the…
In this work, we study the relations between bounded dynamic regret and the classical notion of asymptotic stability for the case of a priori unknown and time-varying cost functions. In particular, we show that bounded dynamic regret…
Model selection in the presence of intractable likelihoods remains a central challenge in Bayesian inference. Approximate Bayesian computation (ABC) provides a flexible likelihood-free framework, but its use for model choice is known to be…
We study the consistency of stochastic dynamic programs under converging probability distributions and other approximations. Utilizing results on the epi-convergence of expectation functions with varying measures and integrands, and the…
We investigate Runge-type approximation theorems for solutions to the 3D unsteady Stokes system. More precisely, we establish that on any compact set with connected complement, local smooth solutions to the 3D unsteady Stokes system can be…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference…