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In many applications, interest focuses on assessing relationships between covariates and the extremes of the distribution of a continuous response. For example, in climate studies, a usual approach to assess climate change has been based on the analysis of annual maximum data. Using the generalized extreme value (GEV) distribution, we can model trends in the annual maximum temperature using the high number of available atmospheric covariates. However, there is typically uncertainty in which of the many candidate covariates should be included. Bayesian methods for variable selection are very useful to identify important covariates. However, such methods are currently very limited for moderately high dimensional variable selection in GEV regression. We propose a Bayesian method for variable selection based on a stochastic search variable selection (SSVS) algorithm proposed for posterior computation. The method is applied to the selection of atmospheric covariates in annual maximum temperature series in three Spanish stations. [ABSTRACT FROM AUTHOR]

There is increasing evidence that global warming manifests itself in more frequent warm days and that heat waves will become more frequent. Presently, a formal definition of a heat wave is not agreed upon in the literature. To avoid this debate, we consider extreme heat events, which, at a given location, are well‐defined as a run of consecutive days above an associated local threshold. Characteristics of extreme heat events (EHEs) are of primary interest, such as incidence and duration, as well as the magnitude of the average exceedance and maximum exceedance above the threshold during the EHE. Using approximately 60‐year time series of daily maximum temperature data collected at 18 locations in a given region, we propose a spatio‐temporal model to study the characteristics of EHEs over time. The model enables prediction of the behaviour of EHE characteristics at unobserved locations within the region. Specifically, our approach employs a two‐state space–time model for EHEs with local thresholds where one state defines above threshold daily maximum temperatures and the other below threshold temperatures. We show that our model is able to recover the EHE characteristics of interest and outperforms a corresponding autoregressive model that ignores thresholds based on out‐of‐sample prediction. [ABSTRACT FROM AUTHOR]