A Spliced Gamma-Generalized Pareto Model for Short-Term Extreme Wind Speed Probabilistic Forecasting

Castro‐Camilo, Daniela; Huser, Raphaël; Rue, Håvard

doi:10.1007/s13253-019-00369-z

Cited by 27 publications

(14 citation statements)

References 40 publications

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“…For the family

{\overline{W}}_{θ^{'}}

, it might correspondingly be appropriate to assume

ν

does not vary over some region or, if that did not suffice to produce stable parameter estimates, to assume

ν, κ_{0}

, and

κ_{1}

do not vary. More recent work on environmental extremes often uses hierarchical models to force the scale and shape parameters of the distribution to vary smoothly in space (Bacro, Gaetan, Opitz, & Toulemonde, 2020; Castro‐Camilo, Huser, & Rue, 2019; Sharkey & Winter, 2019; Yadav et al, 2019) and this approach could also be applied to the parametric families proposed here. Such analyses are usually Bayesian and it is not clear what kinds of priors should be put on the parameters as they vary in some spatial index x .…”

Section: Discussionmentioning

confidence: 99%

A parametric model for distributions with flexible behavior in both tails

Stein

2020

Environmetrics

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Summary For many problems of inference about a marginal distribution function, while the entire distribution is important, extreme quantiles are of particular interest because rare outcomes may have large consequences. In some applications, only the extreme upper quantiles require extra attention, but in, for example, climatological applications, extremes in both tails of the distribution can be impactful. A possible approach in this setting is to use parametric families of distributions that have flexible behavior in both tails. One way to quantify this property is to require that, for any two generalized Pareto distributions, there is a member of the parametric family that behaves like one of the generalized Pareto distributions in the upper tail and like the negative of the other generalized Pareto distribution in the lower tail. This work proposes some specific quantifications of this notion and describes parametric families of distributions that satisfy these specifications. The proposed families all have closed form expressions for their densities and, hence, are convenient for use in practice. A simulation study shows how one of the proposed families can work well for estimating all quantiles when both tails of a distribution are heavy tailed. An application to climate model output shows this family can also work well when applied to daily average January temperature near Calgary, for which the evolving distribution over time due to climate change is difficult to model accurately by any standard parametric family.

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“…For the family

{\overline{W}}_{θ^{'}}

, it might correspondingly be appropriate to assume

ν

does not vary over some region or, if that did not suffice to produce stable parameter estimates, to assume

ν, κ_{0}

, and

κ_{1}

Section: Discussionmentioning

confidence: 99%

A parametric model for distributions with flexible behavior in both tails

Stein

2020

Environmetrics

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“…Another reason is that prediction at unobserved locations may be required, and this can only be achieved with a proper spatial model. To this aim, Bayesian hierarchical models with a Gaussian latent structure are particularly convenient; see, for example, Casson and Coles (1999), Cooley et al (2007), Sang and Gelfand (2009), Cooley and Sain (2010), Turkman, Turkman, and Pereira (2010), , Dyrrdal, Lenkoski, Thorarinsdottir, and Stordal (2015), Geirsson, Hrafnkelsson, and Simpson (2015), Opitz, Huser, Bakka, andRue (2019). Such models, which are the Bayesian analogues of GAMs, can easily handle non-stationarity by embedding covariates into model parameters, as well as different types of latent Gaussian random effects that may be correlated over space and timeoften specified with a sparse precision (i.e., inverse covariance) matrix to speed up computations.…”

Section: Marginal Modeling Of Extremesmentioning

confidence: 99%

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Huser¹,

Wadsworth²

2022

WIREs Computational Stats

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“…Similarly, Turkman et al (2010) fitted Bayesian hierarchical models to spatio-temporal wildfire data from Portugal by taking advantage of MCMC based inference, while Opitz et al (2018) and Castro-Camilo et al (2019) exploited the integrated nested Laplace approximation (INLA) to fit a model to spatio-temporal threshold exceedances. More recently, Hazra et al (2021) proposed using Max-and-Smooth, an approximate Bayesian algorithm designed for extended latent Gaussian models and they applied it to a large-scale extreme precipitation dataset.…”

Section: Introductionmentioning

confidence: 99%

A flexible Bayesian hierarchical modeling framework for spatially dependent peaks-over-threshold data

Yadav¹,

Huser²,

Opitz³

2021

Preprint

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In this work, we develop a constructive modeling framework for extreme threshold exceedances in repeated observations of spatial fields, based on general product mixtures of random fields possessing light or heavy-tailed margins and various spatial dependence characteristics, which are suitably designed to provide high flexibility in the tail and at sub-asymptotic levels. Our proposed model is akin to a recently proposed Gamma-Gamma model using a ratio of processes with Gamma marginal distributions, but it possesses a higher degree of flexibility in its joint tail structure, capturing strong dependence more easily. We focus on constructions with the following three product factors, whose different roles ensure their statistical identifiability: a heavy-tailed spatially-dependent field, a lighter-tailed spatially-constant field, and another lighter-tailed spatially-independent field. Thanks to the model's hierarchical formulation, inference may be conveniently performed based on Markov chain Monte Carlo methods. We leverage the Metropolis adjusted Langevin algorithm (MALA) with random block proposals for latent variables, as well as the stochastic gradient Langevin dynamics (SGLD) algorithm for hyperparameters, in order to fit our proposed model very efficiently in relatively high spatio-temporal dimensions, while simultaneously censoring non-threshold exceedances and performing spatial prediction at multiple sites. The censoring mechanism is applied to the spatially independent component, such that only univariate cumulative distribution functions have to be evaluated. We explore the theoretical prop-

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A Spliced Gamma-Generalized Pareto Model for Short-Term Extreme Wind Speed Probabilistic Forecasting

Cited by 27 publications

References 40 publications

A parametric model for distributions with flexible behavior in both tails

A parametric model for distributions with flexible behavior in both tails

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A flexible Bayesian hierarchical modeling framework for spatially dependent peaks-over-threshold data

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