  Berger et al. (2001) and Ren et al. (2012) derived noninformative priors for
Gaussian process models of spatially correlated data using the reference prior
approach (Berger, Bernardo, 1991). The priors have good statistical properties
and provide a basis for objective Bayesian analysis (Berger, 2006). Using a
trust-region algorithm for optimization with exact equations for posterior
derivatives and an adaptive sparse grid at Chebyshev nodes, this paper develops
deterministic algorithms for fully Bayesian prediction and inference with the
priors. Implementations of the algorithms are available at
https://github.com/rnburn/bbai.
