Modelling the extremal dependence structure of spatial data is considerably
easier if that structure is stationary. However, for data observed over large
or complicated domains, non-stationarity will often prevail. Current methods
for modelling non-stationarity in extremal dependence rely on models that are
either computationally difficult to fit or require prior knowledge of
covariates. Sampson and Guttorp (1992) proposed a simple technique for handling
non-stationarity in spatial dependence by smoothly mapping the sampling
locations of the process from the original geographical space to a latent space
where stationarity can be reasonably assumed. We present an extension of this
method to a spatial extremes framework by considering least squares
minimisation of pairwise theoretical and empirical extremal dependence
measures. Along with some practical advice on applying these deformations, we
provide a detailed simulation study in which we propose three spatial processes
with varying degrees of non-stationarity in their extremal and central
dependence structures. The methodology is applied to Australian summer
temperature extremes and UK precipitation to illustrate its efficacy compared
to a naive modelling approach.
Description
[2101.07167] Spatial deformation for non-stationary extremal dependence
%0 Generic
%1 richards2021spatial
%A Richards, Jordan
%A Wadsworth, Jennifer L.
%D 2021
%K extremalDependence ppt spatial temperature
%R 10.1002/env.2671
%T Spatial deformation for non-stationary extremal dependence
%U http://arxiv.org/abs/2101.07167
%X Modelling the extremal dependence structure of spatial data is considerably
easier if that structure is stationary. However, for data observed over large
or complicated domains, non-stationarity will often prevail. Current methods
for modelling non-stationarity in extremal dependence rely on models that are
either computationally difficult to fit or require prior knowledge of
covariates. Sampson and Guttorp (1992) proposed a simple technique for handling
non-stationarity in spatial dependence by smoothly mapping the sampling
locations of the process from the original geographical space to a latent space
where stationarity can be reasonably assumed. We present an extension of this
method to a spatial extremes framework by considering least squares
minimisation of pairwise theoretical and empirical extremal dependence
measures. Along with some practical advice on applying these deformations, we
provide a detailed simulation study in which we propose three spatial processes
with varying degrees of non-stationarity in their extremal and central
dependence structures. The methodology is applied to Australian summer
temperature extremes and UK precipitation to illustrate its efficacy compared
to a naive modelling approach.
@misc{richards2021spatial,
abstract = {Modelling the extremal dependence structure of spatial data is considerably
easier if that structure is stationary. However, for data observed over large
or complicated domains, non-stationarity will often prevail. Current methods
for modelling non-stationarity in extremal dependence rely on models that are
either computationally difficult to fit or require prior knowledge of
covariates. Sampson and Guttorp (1992) proposed a simple technique for handling
non-stationarity in spatial dependence by smoothly mapping the sampling
locations of the process from the original geographical space to a latent space
where stationarity can be reasonably assumed. We present an extension of this
method to a spatial extremes framework by considering least squares
minimisation of pairwise theoretical and empirical extremal dependence
measures. Along with some practical advice on applying these deformations, we
provide a detailed simulation study in which we propose three spatial processes
with varying degrees of non-stationarity in their extremal and central
dependence structures. The methodology is applied to Australian summer
temperature extremes and UK precipitation to illustrate its efficacy compared
to a naive modelling approach.},
added-at = {2021-06-21T11:50:27.000+0200},
author = {Richards, Jordan and Wadsworth, Jennifer L.},
biburl = {https://www.bibsonomy.org/bibtex/27b54dc66ee45b4ed0c73af7d7a3b1961/simon.brown},
description = {[2101.07167] Spatial deformation for non-stationary extremal dependence},
doi = {10.1002/env.2671},
interhash = {0b8275376cbdb7c7000f4dd602df5bd2},
intrahash = {7b54dc66ee45b4ed0c73af7d7a3b1961},
keywords = {extremalDependence ppt spatial temperature},
note = {cite arxiv:2101.07167Comment: 41 pages, 10 figures},
timestamp = {2021-06-21T11:50:27.000+0200},
title = {Spatial deformation for non-stationary extremal dependence},
url = {http://arxiv.org/abs/2101.07167},
year = 2021
}