A Multi-resolution Gaussian process model for the analysis

5 A multi-resolution model is developed to predict two-dimensional spatial fields based 6 on irregularly spaced observations. The radial basis functions at each level of resolution 7 are constructed using a Wendland compactly supported correlation function with the nodes 8 arranged on a rectangular grid. The grid at each finer level increases by a factor of two 9 and the basis functions are scaled to have a constant overlap. The coefficients associated 10 with the basis functions at each level of resolution are distributed according to a Gaussian 11 Markov random field (GMRF) and take advantage of the fact that the basis is organized 12 as a lattice. Several numerical examples and analytical results establish that this scheme 13 gives a good approximation to standard covariance functions such as the Matérn and also 14 has flexibility to fit more complicated shapes. The other important feature of this model is 15 that it can be applied to statistical inference for large spatial datasets because key matrices 16 in the computations are sparse. The computational efficiency applies to both the evaluation 17 of the likelihood and spatial predictions. 18