Spatial deformation for nonstationary extremal dependence

Richards, J. Ian; Wadsworth, Jennifer L.

doi:10.1002/env.2671

Cited by 7 publications

(4 citation statements)

References 49 publications

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“…For extreme rainfall modelling, Huser and Wadsworth [2019] assume a censored copula for extreme values, targeting the full likelihood for inference, but only for up to 15 locations, noting that a high dimension is a limiting factor for Gaussian copulas, reinforcing the conclusions of Huser et al [2017]. Modelling extreme rainfall through a Brown-Resnick process, Richards and Wadsworth [2021] resort to a composite likelihood approach as an alternative to a computationally unfeasible MLE. More recently, in Richards et al [2022] and Richards et al [2023], authors use a censored Gaussian copula model for the dependence of extreme rainfall events, circumventing the unavailable likelihood by adopting a pseudo-likelihood approach with spatially-informed sub-sampling.…”

Section: Copula Estimation Problemsmentioning

confidence: 99%

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Huk

Adewoyin

Dutta

2023

Preprint

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<p>This work develops a novel method for generating conditional probabilistic rainfall forecasts with temporal and spatial dependence. A two-step procedure is employed. Firstly, marginal location-specific distributions are modelled independently of one another. Secondly, a spatial dependency structure is learned in order to make these marginal distributions spatially coherent. <br />To learn marginal distributions over rainfall values, we propose a class of models termed Joint Generalised Neural Models (JGNMs). These models expand the linear part of generalised linear models with a deep neural network allowing them to take into account non-linear trends of the data while learning the parameters for a distribution over the outcome space.<br />In order to understand the spatial dependency structure of the data, a model based on censored copulas is presented. It is designed for the particularities of rainfall data and incorporates the spatial aspect into our approach. Uniting our two contributions, namely the JGNM and the Censored Spatial Copulas into a single model, we get a probabilistic model capable of generating possible scenarios on short to long-term timescales, able to be evaluated at any given location, seen or unseen. We show an application of it to a precipitation downscaling problem on a large UK rainfall dataset and compare it to existing methods.</p>

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Section: Copula Estimation Problemsmentioning

confidence: 99%

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Huk

Adewoyin

Dutta

2023

Preprint

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“…When covariates are not available, a sensible alternative is the spatial deformation approach first introduced by Sampson and Guttorp (1992). A version of this that is tailored to extremal dependence has recently been proposed by Richards and Wadsworth (2020), adapting methods laid out in Smith (1996); see also Youngman (2020) for further recent work on deformations.…”

Section: Modelmentioning

confidence: 99%

Advances in Statistical Modeling of Spatial Extremes

Huser¹,

Wadsworth²

2020

Preprint

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The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or r-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often suggests that such asymptotic models are too rigidly constrained, and that they do not adequately capture the frequent situation where more severe events tend to be spatially more localized. In other words, these asymptotic models have a strong tail dependence that persists at increasingly high levels, while data usually suggest that it should weaken instead. Another well-known limitation of classical spatial extremes models is that they are either computationally prohibitive to fit in high dimensions, or they need to be fitted using less efficient techniques. In this review paper, we describe recent progress in the modeling and inference for spatial extremes, focusing on new models that have more flexible tail structures that can bridge asymptotic dependence classes, and that are more easily amenable to likelihood-based inference for large datasets. In particular, we discuss various types of random scale constructions, as well as the conditional spatial extremes model, which have recently been getting increasing attention within the statistics of extremes community. We illustrate some of these new spatial models on two different environmental applications.

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“…The analysis of spatio‐temporal data has a rich history in the statistical literature and a wealth of approaches have been proposed; in the context of applications to weather and climate, recent contributions include (Kleiber et al, 2023; Mastrantonio et al, 2019; Mastrantonio et al, 2022; Richards & Wadsworth, 2021), and for a more detailed overview of the field see Liu et al (2021). The methods adopted by different authors vary substantially, since they are tailored to the available data and the question of inferential interest.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian spatio‐temporal model for short‐term forecasting of precipitation fields

et al. 2023

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With extreme weather events becoming more common, the risk posed by surface water flooding is ever increasing. In this work we propose a model, and associated Bayesian inference scheme, for generating short‐term, probabilistic forecasts of localised precipitation on a spatial grid. Our generative hierarchical dynamic model is formulated in discrete space and time with a lattice‐Markov spatio‐temporal auto‐regressive structure, inspired by continuous models of advection and diffusion. Observations from both weather radar and ground based rain gauges provide information from which we can learn the precipitation field through a latent process in addition to unknown model parameters. Working in the Bayesian paradigm provides a coherent framework for capturing uncertainty, both in the underlying model parameters and in our forecasts. Further, appealing to simulation based sampling using MCMC yields a straightforward solution to handling zeros, treated as censored observations, via data augmentation. Both the underlying state and the observations are of moderately large dimension ( and respectively) and this renders standard inference approaches computationally infeasible. Our solution is to embed the ensemble Kalman smoother within a Gibbs sampling scheme to facilitate approximate Bayesian inference in reasonable time. Both the methodology and the effectiveness of our posterior sampling scheme are demonstrated via simulation studies and by a case study of real data from the Urban Observatory project based in Newcastle upon Tyne, UK.

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Spatial deformation for nonstationary extremal dependence

Cited by 7 publications

References 49 publications

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Joint Generalized Neural Models and Censored Spatial Copulas for Probabilistic Rainfall Forecasting

Advances in Statistical Modeling of Spatial Extremes

A Bayesian spatio‐temporal model for short‐term forecasting of precipitation fields

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