The Annals of Applied Statistics

A Markov-switching model for heat waves

Benjamin A. Shaby, Brian J. Reich, Daniel Cooley, and Cari G. Kaufman

Full-text: Open access

Abstract

Heat waves merit careful study because they inflict severe economic and societal damage. We use an intuitive, informal working definition of a heat wave—a persistent event in the tail of the temperature distribution—to motivate an interpretable latent state extreme value model. A latent variable with dependence in time indicates membership in the heat wave state. The strength of the temporal dependence of the latent variable controls the frequency and persistence of heat waves. Within each heat wave, temperatures are modeled using extreme value distributions, with extremal dependence across time accomplished through an extreme value Markov model. One important virtue of interpretability is that model parameters directly translate into quantities of interest for risk management, so that questions like whether heat waves are becoming longer, more severe or more frequent are easily answered by querying an appropriate fitted model. We demonstrate the latent state model on two recent, calamitous, examples: the European heat wave of 2003 and the Russian heat wave of 2010.

Article information

Source
Ann. Appl. Stat., Volume 10, Number 1 (2016), 74-93.

Dates
Received: February 2015
Revised: August 2015
First available in Project Euclid: 25 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1458909908

Digital Object Identifier
doi:10.1214/15-AOAS873

Mathematical Reviews number (MathSciNet)
MR3480488

Zentralblatt MATH identifier
06586137

Keywords
Latent state extremes generalized Pareto distribution extremal dependence

Citation

Shaby, Benjamin A.; Reich, Brian J.; Cooley, Daniel; Kaufman, Cari G. A Markov-switching model for heat waves. Ann. Appl. Stat. 10 (2016), no. 1, 74--93. doi:10.1214/15-AOAS873. https://projecteuclid.org/euclid.aoas/1458909908


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Supplemental materials

  • Additional analysis. The Supplement contains additional exploratory analysis related to the case study, a sensitivity analysis for the prior distribution of the GPD threshold $u$, and results of the model run on 2003 temperatures at several additional sites throughout Western Europe.