A Bayesian non-asymptotic extreme value model for daily rainfall data

Abstract

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 is derived under a set of assumptions different than those used in traditional extreme value (EV) theory. A hierarchical model structure is adopted for capturing the underlying variability in the yearly 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 quantile estimation uncertainty with respect to Bayesian formulations of traditional asymptotic EV methods, particularly in the case of relatively small samples. On the other hand, a negative bias is observed in estimated rainfall quantiles. We evaluate the tradeoff between bias and variance for extreme rainfall quantiles and show that the approach proposed here can be advantageous depending on the sample size available for training. The benefits of the approach are illustrated with an application to a large data set of 479 long daily rainfall historical records from across the conterminous 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, can improve robustness with respect to overfitting to the specific sample in case of short datasets.