Random field priors for spectral density functions

In this paper we discuss how a Gaussian random field with Matérn covariance function can represent our prior uncertainty about the log-spectral density, g(ω), of a Gaussian, short memory time series. Hyperparameters can be suitably tuned in order to determine the mean square differentiability and the range of autocorrelation of the random field g(ω). However, Bayesian computations cannot be easily performed under such prior elicitations. We suggest therefore to approximate the Gaussian random field priors with a class of Gaussian Markov random fields which preserve the main features of the genuine prior distributions.