  To study trends in extreme precipitation across US over the years 1951-2017,
we consider 10 climate indexes that represent extreme precipitation, such as
annual maximum of daily precipitation, annual maximum of consecutive 5-day
average precipitation, which exhibit spatial correlation as well as mutual
dependence. We consider the gridded data, produced by the CLIMDEX project
(http://www.climdex.org/gewocs.html), constructed using daily precipitation
data. In this paper, we propose a multivariate spatial skew-t process for joint
modeling of extreme precipitation indexes and discuss its theoretical
properties. The model framework allows Bayesian inference while maintaining a
computational time that is competitive with common multivariate geostatistical
approaches. In a numerical study, we find that the proposed model outperforms
multivariate spatial Gaussian processes, multivariate spatial t-processes
including their univariate alternatives in terms of various model selection
criteria. We apply the proposed model to estimate the average decadal change in
the extreme precipitation indexes throughout the United States and find several
significant local changes.
