Approximations to the determinant term in gaussian maximum likelihood estimation of some spatial models

Exact Gaussian maximum likelihood estimation for a spatial process requires evaluation of the determinant and inverse of the covariance matrix. If a numerical search is used, numerous evaluations are needed, which will usually be very time consuming. In geographic modelling, it is common to specify the inverse matrix in a simple form, but the evaluation of the determinant can still be slow, even though some simplification may be possible. This paper considers some approximations to the determinant, and their use in estimation.