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March 2018 A multi-resolution model for non-Gaussian random fields on a sphere with application to ionospheric electrostatic potentials
Minjie Fan, Debashis Paul, Thomas C. M. Lee, Tomoko Matsuo
Ann. Appl. Stat. 12(1): 459-489 (March 2018). DOI: 10.1214/17-AOAS1104

Abstract

Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial models for non-Gaussian random fields on a sphere based on a multi-resolution analysis. Using a special wavelet frame, named spherical needlets, as building blocks, the proposed model is constructed in the form of a sparse random effects model. The spatial localization of needlets, together with carefully chosen random coefficients, ensure the model to be non-Gaussian and isotropic. The model can also be expanded to include a spatially varying variance profile. The special formulation of the model enables us to develop efficient estimation and prediction procedures, in which an adaptive MCMC algorithm is used. We investigate the accuracy of parameter estimation of the proposed model, and compare its predictive performance with that of two Gaussian models by extensive numerical experiments. Practical utility of the proposed model is demonstrated through an application of the methodology to a data set of high-latitude ionospheric electrostatic potentials, generated from the LFM-MIX model of the magnetosphere-ionosphere system.

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Minjie Fan. Debashis Paul. Thomas C. M. Lee. Tomoko Matsuo. "A multi-resolution model for non-Gaussian random fields on a sphere with application to ionospheric electrostatic potentials." Ann. Appl. Stat. 12 (1) 459 - 489, March 2018. https://doi.org/10.1214/17-AOAS1104

Information

Received: 1 March 2017; Revised: 1 September 2017; Published: March 2018
First available in Project Euclid: 9 March 2018

zbMATH: 06894714
MathSciNet: MR3773401
Digital Object Identifier: 10.1214/17-AOAS1104

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.12 • No. 1 • March 2018
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