  In order to compute the log-likelihood for high dimensional spatial Gaussian
models, it is necessary to compute the determinant of the large, sparse,
symmetric positive definite precision matrix, Q. Traditional methods for
evaluating the log-likelihood for very large models may fail due to the massive
memory requirements. We present a novel approach for evaluating such
likelihoods when the matrix-vector product, Qv, is fast to compute. In this
approach we utilise matrix functions, Krylov subspaces, and probing vectors to
construct an iterative method for computing the log-likelihood.
