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Gaussian random fields have been one of the most popular tools for analyzingspatial data. However, many geophysical and environmental processes oftendisplay non-Gaussian characteristics. In this paper, we propose a new class ofspatial models for non-Gaussian random fields on a sphere based on amulti-resolution analysis. Using a special wavelet frame, named sphericalneedlets, as building blocks, the proposed model is constructed in the form ofa sparse random effects model. The spatial localization of needlets, togetherwith carefully chosen random coefficients, ensure the model to be non-Gaussianand isotropic. The model can also be expanded to include a spatially varyingvariance profile. The special formulation of the model enables us to developefficient estimation and prediction procedures, in which an adaptive MCMCalgorithm is used. We investigate the accuracy of parameter estimation of theproposed model, and compare its predictive performance with that of twoGaussian models by extensive numerical experiments. Practical utility of theproposed model is demonstrated through an application of the methodology to adata set of high-latitude ionospheric electrostatic potentials, generated fromthe LFM-MIX model of the magnetosphere-ionosphere system.

A Multi-Resolution Model for Non-Gaussian Random Fields on a Sphere with Application to Ionospheric Electrostatic Potentials