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Structural Complexity and Informational Transfer in Spatial Log-Gaussian Cox Processes.

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Summary
This summary is machine-generated.

This study assesses spatial log-Gaussian Cox processes using information theory. It quantifies how stochasticity in the intensity field and point pattern generation affects information transfer and structure.

Keywords:
complexitydivergenceentropyinformation transferspatial log-Gaussian Cox process

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Area of Science:

  • Spatial statistics
  • Information theory
  • Stochastic processes

Background:

  • Log-Gaussian Cox processes (LGCPs) are fundamental for modeling spatial point patterns.
  • Understanding the stochastic mechanisms in LGCPs is crucial for accurate spatial data analysis.
  • Generalized entropy, divergence, and complexity measures offer novel ways to assess stochasticity.

Purpose of the Study:

  • To empirically assess the doubly stochastic mechanism of spatial LGCPs.
  • To characterize the contribution of different phases to overall stochasticity.
  • To analyze information transfer from intensity fields to point patterns.

Main Methods:

  • Empirical assessment using generalized entropy, divergence, and complexity measures.
  • Exploration of Matérn models for log-intensity random fields.
  • Analysis of sensitivity to model and deformation parameters on lattice partitionings.
  • Comparison with reference cases: Poisson process and white noise LGCP.

Main Results:

  • Quantified information transfer and marginal random structure of LGCPs.
  • Demonstrated how entropy, divergence, and complexity measures reflect structural information transfer.
  • Identified the decrease in marginal entropy as a key indicator of the second phase's stochastic effect.

Conclusions:

  • The study provides a quantitative framework for assessing stochasticity in LGCPs.
  • Generalized informational measures effectively discriminate the impact of different stochastic phases.
  • The findings offer insights into the relationship between intensity fields and generated point patterns.