A MULTI-RESOLUTION MODEL FOR NON-GAUSSIAN RANDOM FIELDS ON A SPHERE WITH APPLICATION TO IONOSPHERIC ELECTROSTATIC...

Area of Science:

• Geophysics
• Environmental Science
• Spatial Statistics

Background:

• Gaussian random fields are standard for spatial data analysis.
• Geophysical and environmental processes often exhibit non-Gaussian characteristics, limiting Gaussian models.
• A need for advanced spatial models that capture non-Gaussian features is evident.

Purpose of the Study:

• Propose a new class of spatial models for non-Gaussian random fields on a sphere.
• Utilize spherical needlets for multi-resolution analysis and sparse random effects modeling.
• Develop efficient estimation and prediction procedures for these novel models.

Main Methods:

• Construction of a sparse random effects model using spherical needlets.
• Ensuring non-Gaussian and isotropic properties through needlet localization and random coefficients.
• Development of adaptive Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and prediction.

Main Results:

• The proposed model demonstrates accurate parameter estimation.
• Numerical experiments show superior predictive performance compared to two Gaussian models.
• The model effectively captures non-Gaussian and isotropic spatial characteristics.

Conclusions:

• The novel spherical needlet-based model provides a powerful tool for analyzing non-Gaussian spatial data.
• The methodology is practically useful, as shown by its application to ionospheric electrostatic potential data.
• This approach advances spatial statistics for complex geophysical and environmental phenomena.