A spatial copula interpolation in a random field with application in air pollution data.

Area of Science:

• Environmental Science
• Spatial Statistics
• Geostatistics

Background:

• Interpolating skewed spatial random fields with missing data is challenging without Gaussian assumptions.
• Standard methods struggle with spatial homogeneity, continuity, and boundary points in spatial surfaces.
• Copulas offer a way to model joint tail dependencies beyond Gaussian limitations.

Purpose of the Study:

• To develop a novel spatial interpolation technique for skewed conditional spatial random fields with missing data.
• To introduce a spatial cluster-based C-vine copula model integrated with Expectation-Maximization and Bayesian frameworks.
• To address challenges in spatial homogeneity, continuity, and boundary point interpolation.

Main Methods:

• Developed a spatial cluster-based C-vine copula combined with a modified Gaussian distance kernel.
• Integrated hierarchical clustering, Expectation-Maximization algorithm, and Bayesian inference.
• Employed various parameter estimation techniques for efficient spatial copula interpolation.

Main Results:

• Introduced a novel spatial probability distribution derived from the proposed copula and kernel.
• Demonstrated the effectiveness of the spatial interpolation approach through an application to air pollution data in Delhi.
• Successfully addressed challenges in interpolating skewed spatial fields with missing data and maintaining spatial properties.

Conclusions:

• The proposed spatial cluster-based C-vine copula offers an effective method for interpolating skewed spatial random fields with missing data.
• The novel approach enhances spatial probability distribution estimation, outperforming traditional methods in complex scenarios.
• The technique provides a valuable tool for environmental monitoring and spatial analysis, as shown by the Delhi air pollution case study.