Space–Time Modelling of Extreme Events

Huser, Raphaël; Davison, A. C.

doi:10.1111/rssb.12035

Cited by 165 publications

(183 citation statements)

References 56 publications

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“…showed how temporal heatwave events can be simulated using the conditional extremes framework for a single site. The next step will be to combine these temporal approaches with the spatial approaches outlined in this paper to generate full space-time model on a lattice which incorporate asymptotic independence as well as asymptotic dependence, hence expanding on max-stable spatio-temporal models of Davis et al (2013) and Huser and Davison (2014).…”

Section: Discussionmentioning

confidence: 99%

Modelling the effect of the El Niño-Southern Oscillation on extreme spatial temperature events over Australia

Winter¹,

Tawn²,

Brown³

2016

Ann. Appl. Stat.

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When assessing the risk posed by high temperatures, it is necessary to consider not only the temperature at separate sites but also how many sites are expected to be hot at the same time. Hot events that cover a large area have the potential to put a great strain on health services and cause devastation to agriculture, leading to high death tolls and much economic damage. South-eastern Australia experienced a severe heatwave in early 2009; 374 people died in the state of Victoria and Melbourne recorded its highest temperature since records began in 1859 (Nairn and Fawcett, 2013). One area of particular interest in climate science is the effect of large scale climatic phenomena, such as the El Niño-Southern Oscillation (ENSO), on extreme temperatures. Here, we develop a framework based upon extreme value theory to estimate the effect of ENSO on extreme temperatures across Australia. This approach permits us to estimate the change in temperatures with ENSO at important sites, such as Melbourne, and also whether we are more likely to observe hot temperatures over a larger spatial extent during a particular phase of ENSO. To this end, we design a set of measures that can be used to effectively summarise many important spatial aspects of an extreme temperature event. These measures are estimated using our extreme value framework and we validate whether we can accurately replicate the 2009 Australian heatwave, before using the model to estimate the probability of having a more severe event than has been observed.

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Section: Discussionmentioning

confidence: 99%

Modelling the effect of the El Niño-Southern Oscillation on extreme spatial temperature events over Australia

Winter¹,

Tawn²,

Brown³

2016

Ann. Appl. Stat.

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“…This explains why pairwise likelihoods (Lindsay, 1988;Varin et al, 2011) have become the standard tool for inference in this context (Padoan et al, 2010;Thibaud et al, 2013;Huser and Davison, 2014), although more efficient approaches based on the point process characterization of extremes have recently been proposed (Wadsworth and Tawn, 2014;Engelke et al, 2015;Thibaud and Opitz, 2015;.…”

Section: Introductionmentioning

confidence: 99%

Non-Stationary Dependence Structures for Spatial Extremes

Huser

Genton

2016

JABES

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Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been developed, and fitted to various types of data. However, a recurrent problem is the modeling of non-stationarity. In this paper, we develop non-stationary max-stable dependence structures in which covariates can be easily incorporated. Inference is performed using pairwise likelihoods, and its performance is assessed by an extensive simulation study based on a non-stationary locally isotropic extremal t model. Evidence that unknown parameters are well estimated is provided, and estimation of spatial return level curves is discussed. The methodology is demonstrated with temperature maxima recorded over a complex topography. Models are shown to satisfactorily capture extremal dependence.

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“…Likelihood inference for max-stable models is difficult, since only the bivariate marginal density functions are known in most cases, and pairwise marginal likelihood is typically used (Padoan et al, 2010;Davison and Gholamrezaee, 2012;Huser and Davison, 2012). This raises the question whether some other approach to inference would be preferable.…”

Section: Introductionmentioning

confidence: 99%

“…Kabluchko et al (2009) provided further underpinning for this process by showing that that under mild conditions, the BrownResnick process with variogram 2γ(h) = ( h /ρ) α (ρ > 0, 0 < α ≤ 2), where h is the spatial lag, is essentially the only isotropic limit of properly rescaled maxima of Gaussian processes. The Smith model is obtained by taking a Brown-Resnick process with variogram 2γ(h) = h T Σ −1 h for some covariance matrix Σ, corresponding after an affine transformation to taking α = 2, whereas found that 1/2 < α < 1 for the rainfall data they examined.Likelihood inference for max-stable models is difficult, since only the bivariate marginal density functions are known in most cases, and pairwise marginal likelihood is typically used (Padoan et al, 2010;Davison and Gholamrezaee, 2012;Huser and Davison, 2012). This raises the question whether some other approach to inference would be preferable.…”

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confidence: 99%

Composite likelihood estimation for the Brown-Resnick process

Huser¹,

Davison²

2013

Biometrika

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106

105

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SUMMARY Genton et al. (2011) investigated the gain in efficiency when triplewise, rather than pairwise, likelihood is used to fit the popular Smith max-stable model for spatial extremes. We generalize their results to the Brown-Resnick model and show that the efficiency gain is substantial only for very smooth processes, which are generally unrealistic in applications.Some key words: Brown-Resnick process; Composite likelihood; Max-stable process; Pairwise likelihood; Smith process; Triplewise likelihood. INTRODUCTIONMax-stable processes are useful for the statistical modelling of spatial extreme events. No finite parametrization of such processes exists, but a spectral representation (de Haan, 1984) aids in constructing models. In a 1990 University of Surrey technical report, R. L. Smith proposed a max-stable model based on deterministic storm profiles which has become popular because it is simple, readily interpreted and easily simulated, but unfortunately it is too inflexible for realism in practice. Another popular model, the Brown-Resnick process, is based on intrinsically stationary log-Gaussian processes, can handle a wide range of dependence structures, and often provides a better fit to data; see, for example, or a 2012 University of North Carolina at Chapel Hill PhD thesis by Soyoung Jeon. Kabluchko et al. (2009) provided further underpinning for this process by showing that that under mild conditions, the BrownResnick process with variogram 2γ(h) = ( h /ρ) α (ρ > 0, 0 < α ≤ 2), where h is the spatial lag, is essentially the only isotropic limit of properly rescaled maxima of Gaussian processes. The Smith model is obtained by taking a Brown-Resnick process with variogram 2γ(h) = h T Σ −1 h for some covariance matrix Σ, corresponding after an affine transformation to taking α = 2, whereas found that 1/2 < α < 1 for the rainfall data they examined.Likelihood inference for max-stable models is difficult, since only the bivariate marginal density functions are known in most cases, and pairwise marginal likelihood is typically used (Padoan et al., 2010;Davison and Gholamrezaee, 2012;Huser and Davison, 2012). This raises the question whether some other approach to inference would be preferable. Genton et al. (2011) derived the general form of the likelihood function for the Smith model and showed that large efficiency gains can arise when fitting it using triplewise, rather than pairwise, likelihood. In this paper we extend their investigation to the Brown-Resnick process and show that for rougher models, more realistic than those considered by Genton et al. (2011), the efficiency gains are much less striking. Thus pairwise likelihood inference provides a good compromise between statistical and computational efficiency in many applications.

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Space–Time Modelling of Extreme Events

Cited by 165 publications

References 56 publications

Modelling the effect of the El Niño-Southern Oscillation on extreme spatial temperature events over Australia

Modelling the effect of the El Niño-Southern Oscillation on extreme spatial temperature events over Australia

Non-Stationary Dependence Structures for Spatial Extremes

Composite likelihood estimation for the Brown-Resnick process

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