Wavelet Markov Models as Efficient Alternatives to Tapering and Convolution Fields

The Matérn covariance function is a popular choice for modeling dependence in spatial environmental data. Standard Matérn covariance models are, however, often computationally infeasible for large data sets. In this work, explicit computationally efficient wavelet Markov approximations of Gaussian Matérn fields are derived using Hilbert space approximations. Using a simulation-based study, the wavelet approximations are compared with two of the most popular methods for efficient covariance approximations; covariance tapering, and the convolution-fields method. The methods are compared with respect to their ability to reproduce the Matérn covariance function and their Kriging error when used for spatial prediction. The study indicates that, for a given computational cost, the wavelet Markov methods have a substantial gain in accuracy compared with the other methods.