  Motivated by the analysis of extreme rainfall data, we introduce a general
Bayesian hierarchical model for estimating the probability distribution of
extreme values of intermittent random sequences, a common problem in
geophysical and environmental science settings. The approach presented here
relaxes the asymptotic assumption typical of the traditional extreme value (EV)
theory, and accounts for the possible underlying variability in the
distribution of event magnitudes and occurrences, which are described through a
latent temporal process. Focusing on daily rainfall extremes, the structure of
the proposed model lends itself to incorporating prior geo-physical
understanding of the rainfall process. By means of an extensive simulation
study, we show that this methodology can significantly reduce estimation
uncertainty with respect to Bayesian formulations of traditional asymptotic EV
methods, particularly in the case of relatively small samples. The benefits of
the approach are further illustrated with an application to a large data set of
479 long daily rainfall historical records from across the continental United
States. By comparing measures of in-sample and out-of-sample predictive
accuracy, we find that the model structure developed here, combined with the
use of all available observations for inference, significantly improves
robustness with respect to overfitting to the specific sample.
