High-dimensional modeling of spatial and spatio-temporal conditional extremes using INLA and Gaussian Markov random fields

Emma S. Simpson, Thomas Opitz, Jennifer L. Wadsworth

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The conditional extremes framework allows for event-based stochastic modeling of dependent extremes, and has recently been extended to spatial and spatio-temporal settings. After standardizing the marginal distributions and applying an appropriate linear normalization, certain non-stationary Gaussian processes can be used as asymptotically-motivated models for the process conditioned on threshold exceedances at a fixed reference location and time. In this work, we adapt existing conditional extremes models to allow for the handling of large spatial datasets. This involves specifying the model for spatial observations at d locations in terms of a latent m≪d dimensional Gaussian model, whose structure is specified by a Gaussian Markov random field. We perform Bayesian inference for such models for datasets containing thousands of observation locations using the integrated nested Laplace approximation, or INLA. We explain how constraints on the spatial and spatio-temporal Gaussian processes, arising from the conditioning mechanism, can be implemented through the latent variable approach without losing the computationally convenient Markov property. We discuss tools for the comparison of models via their posterior distributions, and illustrate the flexibility of the approach with gridded Red Sea surface temperature data at over 6,000 observed locations. Posterior sampling is exploited to study the probability distribution of cluster functionals of spatial and spatio-temporal extreme episodes.
Original languageEnglish (US)
StatePublished - Jul 12 2023
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2023-07-18
Acknowledged KAUST grant number(s): OSR-2017-CRG6-3434.02
Acknowledgements: This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-2017-CRG6-3434.02. The sea surface temperature data studied in this paper were provided by GHRSST Met Office and CMEMS.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Economics, Econometrics and Finance (miscellaneous)
  • Statistics and Probability


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