Modelling non-stationary extreme precipitation with max-stable processes and multi-dimensional scaling
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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.
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