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This work addresses the problem of geo-statistical analysis on a linear network by introducing an innovative process based on a moving average construction. The proposed random process generates a valid covariance model, explicitly accounting for the directional dependencies in the domain given by a velocity field. We apply this methodology to real-world data, modeling water temperatures in the Mediterranean Sea under projected climate change scenarios. To preserve the directionality of water currents, we approximate the continuous domain by a linear network. We then construct prediction intervals for temperature projections, providing insights into potential climate impacts on the region.

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A Convolution Process for Spatial Statistical Models on Directed Linear Networks

  • 会议论文

  • 发表日期：

    2025年

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  • Leonardo Marchesin,
  • Alessandra Menafoglio,
  • Piercesare Secchi

摘要

This work addresses the problem of geo-statistical analysis on a linear network by introducing an innovative process based on a moving average construction. The proposed random process generates a valid covariance model, explicitly accounting for the directional dependencies in the domain given by a velocity field. We apply this methodology to real-world data, modeling water temperatures in the Mediterranean Sea under projected climate change scenarios. To preserve the directionality of water currents, we approximate the continuous domain by a linear network. We then construct prediction intervals for temperature projections, providing insights into potential climate impacts on the region.