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Nonparametric spatial models for extremes: application to extreme temperature data

Extremes volume 16, pages 75–101 (2013)Cite this article

Abstract

Estimating the probability of extreme temperature events is difficult because of limited records across time and the need to extrapolate the distributions of these events, as opposed to just the mean, to locations where observations are not available. Another related issue is the need to characterize the uncertainty in the estimated probability of extreme events at different locations. Although the tools for statistical modeling of univariate extremes are well-developed, extending these tools to model spatial extreme data is an active area of research. In this paper, in order to make inference about spatial extreme events, we introduce a new nonparametric model for extremes. We present a Dirichlet-based copula model that is a flexible alternative to parametric copula models such as the normal and t-copula. The proposed modelling approach is fitted using a Bayesian framework that allow us to take into account different sources of uncertainty in the data and models. We apply our methods to annual maximum temperature values in the east-south-central United States.

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Affiliations

  1. Department of Statistics, North Carolina State University (NCSU), Raleigh, NC, USA

    Montserrat Fuentes, John Henry & Brian Reich

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  1. Montserrat Fuentes
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  2. John Henry
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  3. Brian Reich
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Correspondence to Montserrat Fuentes.

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Fuentes, M., Henry, J. & Reich, B. Nonparametric spatial models for extremes: application to extreme temperature data. Extremes 16, 75–101 (2013). https://doi.org/10.1007/s10687-012-0154-1

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  • DOI: https://doi.org/10.1007/s10687-012-0154-1

Keywords

  • Dirichlet processes
  • Extreme temperatures
  • Nonstationarity
  • Return levels
  • Spatial models