Physical processes rarely occur in isolation, rather they influence
and interact with one another. Thus, there is great benefit in modeling potential
dependence between both spatial locations and different processes. It
is the interaction between these two dependencies that is the focus of Genton
and Kleiber’s paper under discussion. We see the problem of ensuring
that any multivariate spatial covariance matrix is nonnegative definite as important,
but we also see it as a means to an end. That “end” is solving the
scientific problem of predicting a multivariate field.