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

Debjoy Thakur1, Ishapathik Das1, Shubhashree Chakravarty2

  • 1Department of Mathematics and Statistics, Indian Institute of Technology, Tirupati, India.

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Summary

This study introduces a novel spatial interpolation method using cluster-based copulas and a modified Gaussian kernel for skewed data with missing values. The technique improves spatial probability distribution estimation, demonstrated with Delhi air pollution data.

Keywords:
Bayesian Spatial Copula InterpolationExpectation-Maximization algorithmHierarchical Spatial ClusteringSpatial Copula InterpolationVon-Mises distribution

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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.