Pairwise copula cyclic graphical model for spatial extremes modeling

Abstract

Research on extreme events modeling has grown in prominence due to the destructive influence and increasing occurrence rate in recent years. In this work, we focus on spatial extremes, where the extreme values measured at different locations are jointly modeled. The resulting model can, for example, be used to describe the occurrence and measure the risk of catastrophes, such as hurricanes and floods in a spatial domain. Moreover, joint analysis of spatial extremes has the potential to forecast the likelihood of extreme events in one location given that has happened elsewhere.

In the proposed model, we leverage the framework of graphical models, which enables compact modeling and efficient inference for large-scale data. We further employ pairwise copulas as the building blocks of the graphical model in order to capture the complex dependence between extreme events. The resulting pairwise copula cyclic graphical model (PCCGM) can therefore flexibly capture the spatial dependence, including the tail parts of the distributions.

Variational Expectation Maximization (EM) algorithm is used to learn the model parameters. By exploiting the particular structure of the proposed model, the proposed algorithm scales gracefully with the dimension of the model. In addition, we develop a sampling algorithm to draw extreme-value samples from the learnt model. Generating extreme-value samples is crucial in practice since extreme events are rare by definition and only the observed samples are insufficient for statistical analysis.

Numerical results show that the learning algorithm can reliably estimate the model parameters. Furthermore, the proposed can preserve tail dependence while fitting the data well.