Environmental contours as Voronoi cells

Hafver, Andreas; Agrell, Christian; Vanem, Erik

doi:10.1007/s10687-022-00437-7

Cited by 10 publications

(4 citation statements)

References 64 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As pointed out in e.g. [6,10], this noise may causes the naive method to fail to satisfy the outreach requirements. For an explanation on why this occurs, we refer to either [6,10] or the discussion around Figure 7.1.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In [10], they discuss how estimation errors in C can lead to the absence of proper contours. To correct this they suggest inflating C by adding a sufficiently large constant, ensuring that the resulting contour is valid, as well as proper with respect to the inflated C. Similarly, in [6], examples of distributions for V are given which allow for no proper contours, regardless of estimation errors. The article also proposes the following method for constructing valid contours in this setting.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Minimal Convex Environmental Contours

Sande,

Wind

2024

The SMAI Journal of Computational Mathematics

View full text Add to dashboard Cite

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimal Convex Environmental Contours

Sande,

Wind

2024

The SMAI Journal of Computational Mathematics

View full text Add to dashboard Cite

“…As pointed out in e.g. [9,6], this noise may causes the naive method to fail to satisfy the outreach requirements. For an explanation on why this occurs, we refer to either [9,6] or the discussion around Figure 5.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In [9], they discuss how estimation errors in C can lead to the absence of proper contours. To correct this they suggest inflating C by adding a sufficiently large constant, ensuring that the resulting contour is valid, as well as proper with respect to the inflated C. Similarly, in [6], examples of distributions for V are given which allow for no proper contours, regardless of estimation errors. The article also proposes the following method for constructing valid contours in this setting.…”

Section: Introductionmentioning

confidence: 99%

Convex environmental contours

et al. 2021

View full text Add to dashboard Cite

Inference for New Environmental Contours Using Extreme Value Analysis

Simpson,

Tawn

2024

JABES

View full text Add to dashboard Cite

Environmental contours are often used in engineering applications to describe risky combinations of variables according to some definition of an exceedance probability. These contours can be used to both understand multivariate extreme events in environmental processes and mitigate against their effects, e.g. in the design of structures. Such ideas are also useful in other disciplines, with the types of extreme events of interest depending on the context. Despite clear connections with extreme value modelling, much of this methodology has so far not been exploited in the estimation of environmental contours; in this work, we provide a way to unify these areas. We focus on the bivariate case, introducing two new definitions of environmental contours. We develop techniques for their inference which exploit a non-standard radial and angular decomposition of the variables, building on previous work for estimating limit sets. Specifically, we model the upper tails of the radial distribution using a generalised Pareto distribution, with adaptable smoothing of the parameters of this distribution. Our methods work equally well for asymptotically independent and asymptotically dependent variables, so do not require us to distinguish between different joint tail forms. Simulations demonstrate reasonable success of the estimation procedure, and we apply our approach to an air pollution data set, which is of interest in the context of environmental impacts on health.Supplementary materials accompanying this paper appear online.

show abstract

Environmental contours as Voronoi cells

Cited by 10 publications

References 64 publications

Minimal Convex Environmental Contours

Minimal Convex Environmental Contours

Convex environmental contours

Inference for New Environmental Contours Using Extreme Value Analysis

Contact Info

Product

Resources

About