  Reference priors are theoretically attractive for the analysis of
geostatistical data since they enable automatic Bayesian analysis and have
desirable Bayesian and frequentist properties. But their use is hindered by
computational hurdles that make their application in practice challenging. In
this work, we derive a new class of default priors that approximate reference
priors for the parameters of some Gaussian random fields. It is based on an
approximation to the integrated likelihood of the covariance parameters derived
from the spectral approximation of stationary random fields. This prior depends
on the structure of the mean function and the spectral density of the model
evaluated at a set of spectral points associated with an auxiliary regular
grid. In addition to preserving the desirable Bayesian and frequentist
properties, these approximate reference priors are more stable, and their
computations are much less onerous than those of exact reference priors. Unlike
exact reference priors, the marginal approximate reference prior of correlation
parameter is always proper, regardless of the mean function or the smoothness
of the correlation function. This property has important consequences for
covariance model selection. An illustration comparing default Bayesian analyses
is provided with a data set of lead pollution in Galicia, Spain.
