相关论文: Marginal and total exceedance probabilities of env…

Environmental contours are an established method in probabilistic engineering design, especially in ocean engineering. The contours help engineers to select the environmental states which are appropriate for structural design calculations.…

Environmental contours are tools frequently used in the early design of marine structures. They provide a description of critical design conditions and serve as a means for simplifying expensive long-term response calculations. Here, we…

Environmental contours are used in structural reliability analysis of marine and coastal structures as an approximate means to locate the boundary of the distribution of environmental variables, and hence sets of environmental conditions…

Extreme value analysis (EVA) uses data to estimate long-term extreme environmental conditions for variables such as significant wave height and period, for the design of marine structures. Together with models for the short-term evolution…

We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood…

We derive a computable closed-form upper bound on the Hausdorff distance between a truncated minimal robust positively invariant (mRPI) set and its infinite-horizon limit. The bound depends only on a disturbance-set size measure and an…

Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…

In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…

We develop a numerical method for the computation of a minimal convex and compact set, $\mathcal{B}\subset\mathbb{R}^N$, in the sense of mean width. This minimisation is constrained by the requirement that $\max_{b\in\mathcal{B}}\langle b ,…

Given finite-dimensional random vectors $Y$, $X$, and $Z$ that form a Markov chain in that order (i.e., $Y \to X \to Z$), we derive upper bounds on the excess minimum risk using generalized information divergence measures. Here, $Y$ is a…

This paper proposes an algorithm to calculate the maximal probability of unsafety with respect to trajectories of a stochastic process and a hazard set. The unsafe probability estimation problem is cast as a primal-dual pair of…

Classical environmental contours are used in structural design in order to obtain upper bounds on the failure probabilities of a large class of designs. Buffered environmental contours serve the same purpose, but with respect to the…

It is often desirable to summarise a probability measure on a space $X$ in terms of a mode, or MAP estimator, i.e.\ a point of maximum probability. Such points can be rigorously defined using masses of metric balls in the small-radius…

An exceedance region is the set of locations in a spatial domain where a process exceeds some threshold. Examples of exceedance regions include areas where ozone concentrations exceed safety standards, there is high risk for tornadoes or…

We study estimation of the proportion of areal units in a spatially correlated domain whose success probabilities exceed a prespecified threshold. Such problems arise in health surveillance, environmental monitoring, and social policy,…

Estimating the parameters of max-stable parametric models poses significant challenges, particularly when some parameters lie on the boundary of the parameter space. This situation arises when a subset of variables exhibits extreme values…

In a low-order model of the general circulation of the atmosphere we examine the predictability of threshold exceedance events of certain observables. The likelihood of such binary events -- the cornerstone also for the categoric (as…

We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…

This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…

We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods,…