  Autoregressive cokriging models have been widely used to emulate multiple
computer models with different levels of fidelity. The dependence structures
are modeled via Gaussian processes at each level of fidelity, where covariance
structures are often parameterized up to a few parameters. The predictive
distributions typically require intensive Monte Carlo approximations in
previous works. This article derives new closed-form formulas to compute the
means and variances of predictive distributions in autoregressive cokriging
models that only depend on correlation parameters. For parameter estimation, we
consider objective Bayesian analysis of such autoregressive cokriging models.
We show that common choices of prior distributions, such as the constant prior
and inverse correlation prior, typically lead to improper posteriors. We also
develop several objective priors such as the independent reference prior and
the independent Jeffreys prior that are shown to yield proper posterior
distributions. This development is illustrated with a borehole function in an
eight-dimensional input space and applied to an engineering application in a
six-dimensional input space.
