Functional Peaks-over-threshold Analysis

Fondeville, Raphaël de; Davison, A. C.

doi:10.48550/arxiv.2002.02711

Cited by 5 publications

(15 citation statements)

References 69 publications

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“…Indeed, both types of rainfall event are driven by different physical laws, producing rain fields with different spatio-temporal structures. The role of risk functional in this case is thus to disentangle both type of extreme events, see de Fondeville and Davison (2021) for a detailed illustration.…”

Section: Principle Of Sampling Designs For Extremesmentioning

confidence: 99%

“…where P is a generalized r-Pareto process; detailed conditions on the functional r can be found in de Fondeville and Davison (2021).…”

Section: Peaks-over-threshold Analysismentioning

confidence: 99%

“…where R is a univariate unit Pareto random variable and W is a stochastic process on the unit L 1 −sphere {x ∈ C(S) : x 1 = 1} whose distribution is determined by Λ and models the dependence of P . Equation ( 10) is a key component to sampling algorithms as the ones described in de Fondeville and Davison (2021). In general, the process W can take any kind of distribution as soon as E{W (s)} = 1 for all s ∈ S.…”

Section: Peaks-over-threshold Analysismentioning

confidence: 99%

“…For instance, if W is log-Gaussian, θ W refers to the parameters of the semi-variogram function γ, which can be allowed to be non-stationary over space. Estimation procedures for a n , b n , ξ and θ W can be found in de Fondeville and Davison (2021) .…”

Section: A Flexible Model For Station Networkmentioning

confidence: 99%

“…Techniques for flood risk quantification, both long and short term, relies on catalogues of heavy rainfall events that are then fed to a hydrological numerical model which translates the event into water runoffs. These catalogues are either historical, i.e., derived from available measurements, or produced by weather generators that can be either numerical (Cloke and Pappenberger, 2009) or stochastic (see, e.g., Furrer and Katz, 2008;de Fondeville and Davison, 2021); in the latter extreme value theory offers a mathematically justified framework to model and extrapolate extreme water levels. In both cases, the methodologies extrapolate stations measurements away from monitoring sites to estimate the water distribution over the region of interest.…”

Section: Introductionmentioning

confidence: 99%

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Optimal sequential sampling design for environmental extremes

de Fondeville,

Wilhelm

2021

Preprint

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The Sihl river, located near the city of Zurich in Switzerland, is under continuous and tight surveillance as it flows directly under the city's main railway station. To issue early warnings and conduct accurate risk quantification, a dense network of monitoring stations is necessary inside the river basin. However, as of 2021 only three automatic stations are operated in this region, naturally raising the question: how to extend this network for optimal monitoring of extreme rainfall events? So far, existing methodologies for station network design have mostly focused on maximizing interpolation accuracy or minimizing the uncertainty of some model's parameters estimates. In this work, we propose new principles inspired from extreme value theory for optimal monitoring of extreme events. For stationary processes, we study the theoretical properties of the induced sampling design that yields non-trivial point patterns resulting from a compromise between a boundary effect and the maximization of inter-location distances. For general applications, we propose a theoretically justified functional peak-overthreshold model and provide an algorithm for sequential station selection. We then issue recommendations for possible extensions of the Sihl river monitoring network, by efficiently leveraging both station and radar measurements available in this region.

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Section: Principle Of Sampling Designs For Extremesmentioning

confidence: 99%

“…where P is a generalized r-Pareto process; detailed conditions on the functional r can be found in de Fondeville and Davison (2021).…”

Section: Peaks-over-threshold Analysismentioning

confidence: 99%

Section: Peaks-over-threshold Analysismentioning

confidence: 99%

Section: A Flexible Model For Station Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal sequential sampling design for environmental extremes

de Fondeville,

Wilhelm

2021

Preprint

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Semi-parametric resampling with extremes

2021

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Nonparametric resampling methods such as Direct Sampling are powerful tools to simulate new datasets preserving important data features such as spatial patterns from observed or analogue datasets while using only minimal assumptions. However, such methods cannot generate extreme events beyond the observed range of data values. We here propose using tools from extreme value theory for stochastic processes to extrapolate observed data towards yet unobserved high quantiles. Original data are first enriched with new values in the tail region, and then classical resampling algorithms are applied to enriched data. In a first approach to enrichment that we label "naive resampling", we generate an independent sample of the marginal distribution while keeping the rank order of the observed data. We point out inaccuracies of this approach around the most extreme values, and therefore develop a second approach that works for datasets with many replicates. It is based on the asymptotic representation of extreme events through two stochastically independent components: a magnitude variable, and a profile field describing spatial variation. To generate enriched data, we fix a target range of return levels of the magnitude variable, and we resample magnitudes constrained to this range. We then use the second approach to generate heatwave scenarios of yet unobserved magnitude over France, based on daily temperature reanalysis training data for the years 2010 to 2016.

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High-dimensional modeling of spatial and spatio-temporal conditional extremes using INLA and Gaussian Markov random fields

Simpson¹,

Opitz²,

Wadsworth³

2020

Preprint

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The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial and spatio-temporal settings. After standardizing the marginal distributions and applying an appropriate linear normalization, certain non-stationary Gaussian processes can be used as asymptotically-motivated models for the process conditioned on threshold exceedances at a fixed reference location and time. In this work, we adopt a Bayesian perspective by implementing estimation through the integrated nested Laplace approximation (INLA), allowing for novel and flexible semi-parametric specifications of the Gaussian mean function. By using Gauss-Markov approximations of the Matérn covariance function (known as the Stochastic Partial Differential Equation approach) at a latent stage of the model, likelihood-based inference becomes feasible even with several thousands of observed locations. We explain how constraints on the spatial and spatio-temporal Gaussian processes, arising from the conditioning mechanism, can be implemented through the latent variable approach without losing the computationally convenient Markov property. We discuss tools for the comparison of posterior models, and illustrate the flexibility of the approach with gridded Red Sea surface temperature data at over 6, 000 observed locations. Posterior sampling is exploited to study the probability distribution of cluster functionals of spatial and spatio-temporal extreme episodes.

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Functional Peaks-over-threshold Analysis

Cited by 5 publications

References 69 publications

Optimal sequential sampling design for environmental extremes

Optimal sequential sampling design for environmental extremes

Semi-parametric resampling with extremes

High-dimensional modeling of spatial and spatio-temporal conditional extremes using INLA and Gaussian Markov random fields

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