  Impact assessment of natural hazards requires the consideration of both
extreme and non-extreme events. Extensive research has been conducted on the
joint modeling of bulk and tail in univariate settings; however, the
corresponding body of research in the context of multivariate analysis is
comparatively scant. This study extends the univariate joint modeling of bulk
and tail to the multivariate framework. Specifically, it pertains to cases
where multivariate observations exceed a high threshold in at least one
component. We propose a multivariate mixture model that assumes a parametric
model to capture the bulk of the distribution, which is in the max-domain of
attraction (MDA) of a multivariate extreme value distribution (mGEVD). The tail
is described by the multivariate generalized Pareto distribution, which is
asymptotically justified to model multivariate threshold exceedances. We show
that if all components exceed the threshold, our mixture model is in the MDA of
an mGEVD. Bayesian inference based on multivariate random-walk
Metropolis-Hastings and the automated factor slice sampler allows us to
incorporate uncertainty from the threshold selection easily. Due to
computational limitations, simulations and data applications are provided for
dimension $d=2$, but a discussion is provided with views toward scalability
based on pairwise likelihood.
