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Extremes

, Volume 13, Issue 4, pp 375–397 | Cite as

Asymptotic models and inference for extremes of spatio-temporal data

  • Kamil Feridun Turkman
  • M. A. Amaral Turkman
  • J. M. Pereira
Article

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.

Keywords

Bayesian hierarchical models Generalized Pareto distribution Wildfires 

AMS 2000 Subject Classifications

60G70 62F15 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Kamil Feridun Turkman
    • 1
  • M. A. Amaral Turkman
    • 1
  • J. M. Pereira
    • 2
  1. 1.CEAUL and DEIO, FCULUniversity of LisbonLisbonPortugal
  2. 2.ISA Technical University of LisbonLisbonPortugal

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