  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.
