Asymptotic models and inference for extremes of spatio-temporal data

Abstract

Recently there has been a lot of effort to model extremes of spatially dependent data. These efforts seem to be divided into two distinct groups: the study of max-stable processes, together with the development of statistical models within this framework; the use of more pragmatic, flexible models using Bayesian hierarchical models (BHM) and simulation based inference techniques. Each modeling strategy has its strong and weak points. While max-stable models capture the local behavior of spatial extremes correctly, hierarchical models based on the conditional independence assumption, lack the asymptotic arguments the max-stable models enjoy. On the other hand, they are very flexible in allowing the introduction of physical plausibility into the model. When the objective of the data analysis is to estimate return levels or kriging of extreme values in space, capturing the correct dependence structure between the extremes is crucial and max-stable processes are better suited for these purposes. However when the primary interest is to explain the sources of variation in extreme events Bayesian hierarchical modeling is a very flexible tool due to the ease with which random effects are incorporated in the model. In this paper we model a data set on Portuguese wildfires to show the flexibility of BHM in incorporating spatial dependencies acting at different resolutions.

Nonstationarity in peaks‐over‐threshold river flows: A regional random effects model

“…In the most frequently used such model, the spatial random effects associated with each distribution parameter have a Gaussian process hyperprior. The covariance function of the Gaussian process decays with separation distance; for further details, see the reviews in Turkman et al (), Cooley et al (), and Davison, Padoan, and Ribatet (). Consequently, marginal parameters and related quantities such as return levels vary smoothly over space.…”

“…Consequently, marginal parameters and related quantities such as return levels vary smoothly over space. Such models have been used to model hurricane wind speeds (Casson & Coles, ), ozone levels (Gilleland et al, ), precipitation (Cooley et al, ; Cooley & Sain, ; Jonathan et al, ; Sang & Gelfand, ; Wang & So, ), and wildfire (Mendes, de Zea Bermudez, Pereira, Turkman, & Vasconcelos, ; Turkman et al, ).…”

“…Temporal nonstationarity has been modelled using temporal random effects (Eastoe & Tawn, ; Fawcett & Walshaw, ; Turkman et al, ) and dynamic linear models (do Nascimento, Gamerman, & Lopes, ; Huerta & Sansó, ; Wei & Huerta, ). Eastoe and Tawn () and Turkman et al () use an autoregressive model for the random effects in a Poisson and GP model respectively. Fawcett and Walshaw (), who also fit a GP model, use a hyperprior in which the mean of each monthly random effect is the average of the random effects for the previous and following months.…”

“…In the statistical literature, random effects models for spatiotemporal environmental data have been implemented in a Bayesian hierarchical modelling framework (Casson & Coles, ; Cooley, Nychka, & Naveau, ; Jonathan, Favre, Blisle, & Angers, ; Turkman, Turkman, & Pereira, ; Wang & So, ). The random effects, also known as latent processes, are given a hyperprior that generates a spatiotemporal structure in the parameters of the marginal (site‐specific) model.…”

Toward enhanced understanding and projections of climate extremes using physics-guided data mining techniques

“…Hence, multivariate statistical approaches are often necessary in order to completely assess risk of hydrological extremes. Further developments in the statistical theories related to multivariate extremes are needed for advancing our ability to quantify the complex dependencies of climate extremes more completely, and with greater certainty (Kuhn et al, 2012;Marty and Blanchet, 2011;Mastrandrea et al, 2011;Turkman et al, 2009;Wadsworth and Tawn, 2012). Descriptions of rainfall extremes, whether based on EVT or fixed/dynamic thresholds, need to characterize changing statistics of storm events Ganguly, 2011), droughts (van Huijgevoort et al, 2012) and be relevant to multiple sectors, including hydraulic infrastructure design, flood and drought management policy.…”