A Censored Bayesian Hierarchical Model For Precipitation

TL;DR

This paper introduces a censored Bayesian hierarchical model using generalized hyperbolic distributions to effectively model entire rainfall distributions, including extremes and zeros, providing improved tail estimates over traditional methods.

Contribution

It proposes a novel flexible hierarchical model that captures the full rainfall distribution with better tail estimation without threshold selection.

Findings

Narrower credible intervals for rainfall extremes compared to GP models

Accurately fits entire rainfall distribution including zeros and heavy tails

Efficiently models short-term dependencies in rainfall data

Abstract

Modelling of precipitation, including extremes, is important for hydrological and agricultural applications. Traditionally, because of large sample properties for data over a large threshold value, generalised Pareto (GP) distributions are often used for modelling extreme rainfall. It can be shown that under certain conditions the generalised hyperbolic (GH) distributions can approximate the power law decay of the GP distribution in the tails. Given their flexible form, this raises the possibility that distributions from the GH family serve as a model for the entire rainfall distribution thus avoiding the need to select a threshold. In this paper, we use a flexible censored hierarchical model that leverages the GH distribution to accommodate data subject to heavy tails and an excessive number of zeros. The fitted model allows estimation of probabilities and return periods of the rainfall extremes, and it produces narrower credible intervals in the tails than the traditional GP method. The model not only fits the tails of the rainfall distribution, but fits the whole distribution very well. It also efficiently represents short-term dependencies in the data so it is suitable for evaluating duration over and below thresholds as well as duration of zero rainfall.