Approximate likelihood for large irregularly spaced spatial data.

Area of Science:

• Spatial statistics
• Geostatistics
• Computational statistics

Background:

• Exact likelihood calculations for large spatial datasets are computationally infeasible, often requiring O(n^3) operations.
• Gaussian spatial processes are commonly used for modeling spatial data, but computational challenges limit their application to large, irregularly spaced datasets.
• Missing values in spatial data further complicate likelihood-based analyses.

Purpose of the Study:

• To develop a computationally efficient approximation to the Gaussian log likelihood for spatial data.
• To address challenges posed by large, irregularly spaced datasets and the presence of missing values.
• To enable the analysis of complex spatial structures in large-scale environmental datasets.

Main Methods:

• Utilized Whittle's approximation for Gaussian log likelihood estimation.
• Developed a method applicable to spatial regular lattices with missing values and irregularly spaced datasets.
• Achieved a computational complexity of O(n log(2)n), significantly reducing computational burden.

Main Results:

• The proposed method demonstrates significant computational advantages over exact likelihood calculations.
• Simulations and theoretical analyses confirm the method's efficiency and performance for spatial likelihood approximation.
• The approach effectively handles irregularly spaced data and missing values.

Conclusions:

• Whittle's approximation offers a feasible and efficient solution for likelihood-based spatial analysis of large datasets.
• The method is robust for both regular and irregularly spaced spatial data, including those with missing observations.
• Successfully applied to estimate spatial structure in satellite-derived sea surface temperature (SST) data.