Hierarchical Transformed Scale Mixtures for Flexible Modeling of Spatial Extremes on Datasets with Many Locations

Abstract

Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity of repeatedly evaluating the multivariate Gaussian distribution function. In this work, we attempt to achieve truly high-dimensional inference for extremes of spatial processes, while retaining the desirable flexibility in the tail dependence structure, by modifying an established class of models based on scale mixtures Gaussian processes. We show that the desired extremal dependence properties from the original models are preserved under the modification, and demonstrate that the corresponding Bayesian hierarchical model does not involve the expensive computation of the multivariate Gaussian distribution function. We fit our model to exceedances of a high threshold, and perform coverage analyses and cross-model checks to validate its ability to capture different types of tail characteristics. We use a standard adaptive Metropolis algorithm for model fitting, and further accelerate the computation via parallelization and Rcpp. Lastly, we apply the model to a dataset of a fire threat index on the Great Plains region of the US, which is vulnerable to massively destructive wildfires. We find that the joint tail of the fire threat index exhibits a decaying dependence structure that cannot be captured by limiting extreme value models.

References in corpus (4)

• HadISD: a quality-controlled global synoptic report database for selected variables at long-term stations from 1973--2011
• Efficient inference and simulation for elliptical Pareto processes
• The generalized Pareto process; with a view towards application and simulation
• Modeling asymptotically independent spatial extremes based on Laplace random fields

Cited by in corpus (5)

• A Deep Learning Synthetic Likelihood Approximation of a Non-stationary Spatial Model for Extreme Streamflow Forecasting
• High-dimensional modeling of spatial and spatio-temporal conditional extremes using INLA and Gaussian Markov random fields
• Flexible space-time models for extreme data
• Computationally Scalable Bayesian SPDE Modeling for Censored Spatial Responses
• A Dimension-Reduced Multivariate Spatial Model for Extreme Events: Balancing Flexibility and Scalability