Modelling non-stationary extreme precipitation with max-stable processes and multi-dimensional scaling
share
Modeling the joint distribution of extreme weather events in several locations is a challenging topic with important applications. We study extreme daily precipitation events in Switzerland through the use of max-stable models. The non-stationarity of the spatial process at hand involves important challenges, which are typically dealt with by using a stationary model in a so-called climate space, with well-chosen covariates. Here, we instead chose to warp the weather stations under study in a latent space of higher dimension using Multidimensional Scaling (MDS). The advantage of this approach is its improved flexibility to reproduce highly non-stationary phenomena; while keeping a spatial model. Interpolating the MDS mapping enables to place any location in the latent space, thus reproducing non-stationarity in the initial (longitude,latitude,elevation) space. Two model fitting approaches, which both use MDS, are presented and compared to a classical approach which relies on composite likelihood maximization in a climate space. An application in insurance is shown, where one aims at modeling the distribution of the number of stations hit by extreme precipitations during the same year.
READ FULL TEXT