The Annals of Applied Statistics

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, and Tomoko Matsuo

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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.

Article information

Source
Ann. Appl. Stat. Volume 12, Number 1 (2018), 459-489.

Dates
Received: March 2017
Revised: September 2017
First available in Project Euclid: 9 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1520564480

Digital Object Identifier
doi:10.1214/17-AOAS1104

Keywords
Non-Gaussian random field multi-resolution analysis isotropic process on a sphere MCMC ionospheric electrostatic potential LFM-MIX model

Citation

Fan, Minjie; Paul, Debashis; Lee, Thomas C. M.; Matsuo, Tomoko. A multi-resolution model for non-Gaussian random fields on a sphere with application to ionospheric electrostatic potentials. Ann. Appl. Stat. 12 (2018), no. 1, 459--489. doi:10.1214/17-AOAS1104. https://projecteuclid.org/euclid.aoas/1520564480


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Supplemental materials

  • Supplement to “A multi-resolution model for non-Gaussian random fields on a sphere with application to ionospheric electrostatic potentials”. This supplement provides additional figures and details of the numerical experiments and application.