  Gaussian stochastic process (GaSP) has been widely used in two fundamental
problems in uncertainty quantification, namely the emulation and calibration of
mathematical models. Some objective priors, such as the reference prior, are
studied in the context of emulating (approximating) computationally expensive
mathematical models. In this work, we introduce a new class of priors, called
the jointly robust prior, for both the emulation and calibration. This prior is
designed to maintain various advantages from the reference prior. In emulation,
the jointly robust prior has an appropriate tail decay rate as the reference
prior, and is computationally simpler than the reference prior in parameter
estimation. Moreover, the marginal posterior mode estimation with the jointly
robust prior can separate the influential and inert inputs in mathematical
models, while the reference prior does not have this property. We establish the
posterior propriety for a large class of priors in calibration, including the
reference prior and jointly robust prior in general scenarios, but the jointly
robust prior is preferred because the calibrated mathematical model typically
predicts the reality well. The jointly robust prior is used as the default
prior in two new R packages, called "RobustGaSP" and "RobustCalibration",
available on CRAN for emulation and calibration, respectively.
