  Modeling the joint distribution of extreme weather events in multiple
locations is a challenging task with important applications. In this study, we
use max-stable models to study extreme daily precipitation events in
Switzerland. The non-stationarity of the spatial process at hand involves
important challenges, which are often 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 tractable stationary spatial model in the latent space. Two model
fitting approaches, which both use MDS, are presented and compared to a
classical approach that relies on composite likelihood maximization in a
climate space. Results suggest that the proposed methods better reproduce the
observed extremal coefficients and their complex spatial dependence.
