  How to include censored data in a statistical analysis is a recur-rent issue
in statistics. In multivariate extremes, the dependence structure of large
observations can be characterized in terms of a non parametric angular measure,
while marginal excesses above asymptotically large thresholds have a parametric
distribution. In this work, a flexible semi-parametric Dirichlet mix-ture model
for angular measures is adapted to the context of censored data and missing
components. One major issue is to take into account censoring intervals
overlapping the extremal threshold, without knowing whether the correspond-ing
hidden data is actually extreme. Further, the censored likelihood needed for
Bayesian inference has no analytic expression. The first issue is tackled using
a Poisson process model for extremes, whereas a data augmentation scheme avoids
multivariate integration of the Poisson process intensity over both the
censored intervals and the failure region above threshold. The implemented MCMC
algorithm allows simultaneous estimation of marginal and dependence parameters,
so that all sources of uncertainty other than model bias are cap-tured by
posterior credible intervals. The method is illustrated on simulated and real
data.
