Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction.

Area of Science:

• Environmental science
• Geostatistics
• Statistical modeling

Background:

• Standard Gaussian process models often fail to capture complex spatial field characteristics.
• Non-Gaussian spatial data requires advanced modeling techniques for accurate reconstruction.
• Environmental monitoring and sensor networks generate data with non-Gaussian properties.

Purpose of the Study:

• To explore a class of non-Gaussian spatial random field models using Tukey g-and-h transformations.
• To develop and evaluate flexible spatial field reconstruction methods for environmental applications.
• To characterize the statistical properties of Tukey g-and-h warped Gaussian processes.

Main Methods:

• Utilized Tukey g-and-h transformations to create warped spatial Gaussian process models.
• Derived five multi-point estimators: MMSE, MAP, S-BLUE, Spatial Regional, and Level Exceedance.
• Applied simulation studies and real environmental monitoring data for validation.

Main Results:

• Tukey g-and-h warped Gaussian processes provide flexible marginal distributions (skewed, leptokurtic, heavy-tailed).
• Developed novel estimators for spatial field reconstruction, including threshold exceedance methods.
• Demonstrated superior performance of Tukey g-and-h models over standard Gaussian models in a real data application.

Conclusions:

• Tukey g-and-h transformations offer a powerful approach for modeling non-Gaussian spatial fields.
• The proposed flexible models and estimators enhance spatial field reconstruction accuracy in environmental monitoring.
• This methodology provides a significant advancement for analyzing complex spatial data in sensor networks.