Maximum likelihood estimation of noisy Gaussian Markov random fields

In this paper we consider the issues involved in signal extraction and parameter estimation of particular spatial and spatio temporal processes observed with additive Gaussian noise. Within spatial statistics, we discuss maximum likelihood estimation of noisy auto-Gaussian models. For large lattices the estimation method can be computationally demanding thus, we present a maximum likelihood estimator which can be computed in O(n²) steps. Spatio temporal processes are of main interest and parameter estimation of the STARG+Noise model class is also considered. The statistical properties of the proposed maximum likelihood estimator are finally explored in a simulation study.