The relation between and may be modelled over distance bands (e.g. vianon-linear regression) involving parametric forms such as above.
However, there are drawbacks to such procedures (Diggle and Ribeiro, 2002), and Bayesian approaches to spatial covariance generally focus on likelihood based estimation and interpolation (Ecker and Gelfand, 1997). For the linear model
the log-likelihood kernel is
Identifiability of parameters may be improved (and sampling reduced) by discrete priors for the range parameter , or on the nugget to sill ratio in the reparameterized covariance matrix (Diggle and Ribeiro, 2007, Chapter 7; Diggle et al., 2003, p. 65). Modifications of this likelihood ...