Convolution models for nonstationary spatial data

A simple Bayesian model for a univariate spatial Gaussian process can be defined as follows. The quantity of interest will be denoted {Z(s), s ∈ G}, G ⊂ R (d is the dimension of the spatial domain, here d = 2), which is the observed value of Y (s), a latent spatial process. Furthermore, suppose we have observations which are a partial realization of this random process, taken at a fixed, finite set of n spatial locations {s1, ..., sn} ∈ G, giving the random (observed) vector Z = (Z(s1), ..., Z(sn)) , which will be assumed to have a multivariate Gaussian distribution, conditional on the unobserved latent process. Specifically,