An approximate likelihood function of spatial correlation parameters

Even under assumption of normality, likelihood-based inferences are often difficult for large and irregularly spaced spatial datasets. Exact calculations of the likelihood for a Gaussian spatial process observed in n locations require O ( n 3 ) operations. Instead of Whittle’s approximation to the Gaussian log likelihood for large spatial datasets, this paper introduces an approximated likelihood function of spatial parameters based on the correlogram, which involves no calculation of determinants and is computationally feasible. The proposed likelihood approximation method for spatial parameter is applied to the estimation of the spatial structure of changes in the average summer temperature based on 30 years of data by using an regional climate model (RCM) with a particular global climate model (GCM) boundary condition. The results verify the benefits and the performance of the proposed method.