Spectral approximation to the likelihood for an intrinsic Gaussian random field

Intrinsic Gaussian random fields generated by conditional autoregressive mo dels are considered. A spectral approximation to the log-likelihood functio n of an intrinsic random field was given by Kunsch. Here a rigorous treatme nt is given of the comparison between the exact and spectral log-likelihood functions as the domain of observations increases. (C) 1999 Academic Press .