Spatial Regression Models for Extremes (original) (raw)
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Spatio-temporal models for large-scale indicators of extreme weather
Environmetrics, 2011
Extreme weather events such as thunderstorms and tornadoes are of great concern as these events pose a significant threat to life, property, and economic stability. Because of the difficulty of gathering data on extreme events, this paper proposes modeling the conditions for extreme weather through large-scale indicators. The advantage of using large-scale indicators is that climate models can be used to generate data whereas climate models cannot generate data on extreme events themselves. This paper focuses on comparing spatio-temporal models for reanalysis data of large-scale indicators for extreme weather observed across the continental United States and Mexico. Results indicate that rigorous treatment of spatial and temporal dynamics is necessary. The models find that the intensity of conditions for extreme weather is particularly high for the central United States and the intensity of these conditions is increasing over time but the amount of increase may not be practically significant.
A survey of spatial extremes: Measuring spatial dependence and modeling spatial effects
2012
We survey the current practice of analyzing spatial extreme data, which lies at the intersection of extreme value theory and geostatistics. Characterizations of multivariate max-stable distributions typically assume specific univariate marginal distributions, and their statistical applications generally require capturing the tail behavior of the margins and describing the tail dependence among the components. We review current methodology for spatial extremes analysis, discuss the extension of the finite-dimensional extremes framework to spatial processes, review spatial dependence metrics for extremes, survey current modeling practice for the task of modeling marginal distributions, and then examine max-stable process models and copula approaches for modeling residual spatial dependence after accounting for marginal effects.
Exploration and Inference in Spatial Extremes Using Empirical Basis Functions
Journal of Agricultural, Biological and Environmental Statistics, 2019
Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to explore and model spatial extremal dependence. Based on a low-rank max-stable model we propose a data-driven approach to estimate meaningful basis functions using empirical pairwise extremal coefficients. These spatial empirical basis functions can be used to visualize the main trends in extremal dependence. In addition to exploratory analysis, we describe how these functions can be used in a Bayesian hierarchical model to model spatial extremes of large datasets. We illustrate our methods on extreme precipitations in eastern U.S.
Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain
Water Resources Research
We propose a Bayesian hierarchical model for spatial extremes on a large domain. In the data layer a Gaussian elliptical copula having generalized extreme value (GEV) marginals is applied. Spatial dependence in the GEV parameters are captured with a latent spatial regression with spatially varying coefficients. Using a composite likelihood approach, we are able to efficiently incorporate a large precipitation dataset, which includes stations with missing data. The model is demonstrated by application to fall precipitation extremes at approximately 2600 stations covering the western United States, −125E to −100E longitude and 30N to 50N latitude. The hierarchical model provides GEV parameters on a 1/8th degree grid and consequently maps of return levels and associated uncertainty. The model results indicate that return levels vary coherently both spatially and across seasons, providing information about the space-time variations of risk of extreme precipitation in the western US, helpful for infrastructure planning.
A Bayesian semi-parametric hybrid model for spatial extremes with unknown dependence structure
2020
The max-stable process is an asymptotically justified model for spatial extremes. In particular, we focus on the hierarchical extreme-value process (HEVP), which is a particular max-stable process that is conducive to Bayesian computing. The HEVP and all max-stable process models are parametric and impose strong assumptions including that all marginal distributions belong to the generalized extreme value family and that nearby sites are asymptotically dependent. We generalize the HEVP by relaxing these assumptions to provide a wider class of marginal distributions via a Dirichlet process prior for the spatial random effects distribution. In addition, we present a hybrid max-mixture model that combines the strengths of the parametric and semi-parametric models. We show that this versatile max-mixture model accommodates both asymptotic independence and dependence and can be fit using standard Markov chain Monte Carlo algorithms. The utility of our model is evaluated in Monte Carlo sim...
On Estimation and Prediction of Simple Model and Spatial Hierarchical Model for Temperature Extremes
2017 International Conference on Soft Computing, Intelligent System and Information Technology (ICSIIT), 2017
A simple independent generalized extreme value (GEV) model and a three-stage hierarchical model were applied to regional climate model outputs for temperature extremes over Tasmania, Australia. The parameters of each model were estimated using a maximum likelihood and a hybrid Markov chain Monte Carlo (MCMC) approach respectively. The two models were compared based on how well the models could predict extremes for 50 randomly selected locations that were withheld from fitting, using root mean squared prediction error (RMSPE), ten times. The RMSPEs of the two models show that the three-stage hierarchical model outperformed the simple model. We showed that the spatial hierarchical model has successfully smoothed the shape parameters. The high values tend to be pulled down, the low values to be pushed up.
Latent Gaussian Models for High-Dimensional Spatial Extremes
2021
In this chapter, we show how to efficiently model high-dimensional extreme peaksover-threshold events over space in complex non-stationary settings, using extended latent Gaussian Models (LGMs), and how to exploit the fitted model in practice for the computation of long-term return levels. The extended LGM framework assumes that the data follow a specific parametric distribution, whose unknown parameters are transformed using a multivariate link function and are then further modeled at the latent level in terms of fixed and random effects that have a joint Gaussian distribution. In the extremal context, we here assume that the data level distribution is described in terms of a Poisson point process likelihood, motivated by asymptotic extreme-value theory, and which conveniently exploits information from all threshold exceedances. This contrasts with the more common data-wasteful approach based on block maxima, which are typically modeled with the generalized extreme-value (GEV) dist...
Modeling Extreme Events in Spatial Domain by Copula Graphical Models
We propose a new statistical model that captures the conditional dependence among extreme events in a spatial domain. This model may for instance be used to describe catastrophic events such as earthquakes, floods, or hurricanes in certain regions, and in particular to predict extreme values at unmonitored sites. The proposed model is derived as follows. The block maxima at each location are assumed to follow a Generalized Extreme Value (GEV) distribution. Spatial dependence is modeled in two complementary ways. The GEV parameters are coupled through a thin-membrane model, a specific type of Gaussian graphical model often used as smoothness prior. The extreme events, on the other hand, are coupled through a copula Gaussian graphical model with the precision matrix corresponding to a (generalized) thin-membrane model. We then derive inference and interpolation algorithms for the proposed model. The approach is validated on synthetic data as well as real data related to hurricanes in the Gulf of Mexico. Numerical results suggest that it can accurately describe extreme events in spatial domain, and can reliably interpolate extreme values at arbitrary sites.
Environmetrics, 2012
We propose an approach to modeling and risk assessment for extremes of environmental processes evolving over time and recorded at a number of spatial locations. We follow an extension of the point process approach to analysis of extremes under which the times of exceedances over a given threshold are assumed to arise from a non-homogeneous Poisson process. To achieve flexible shapes and temporal heterogeneity for the intensity of extremes at any particular spatial location, we utilize a logit-normal mixture model for the corresponding Poisson process density. A spatial Dirichlet process prior for the mixing distributions completes the nonparametric spatio-temporal model formulation. We discuss methods for posterior simulation, using Markov chain Monte Carlo techniques, and develop inference for spatial interpolation of risk assessment quantities for high-level exceedances of the environmental process. The methodology is tested with a synthetic data example and is further illustrated with analysis of rainfall exceedances recorded over a period of 50 years from a region in South Africa.