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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
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Bayesian Modeling for Nonstationary Spatial Point Process via Spatial Deformations.

Dani Gamerman1, Marcel de Souza Borges Quintana1,2, Mariane Branco Alves1

  • 1DME-Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-909, RJ, Brazil.

Entropy (Basel, Switzerland)
|August 29, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a novel spatial Cox process model using data-driven spatial deformation to capture nonstationary patterns. The enhanced method improves modeling of complex spatial phenomena, outperforming alternatives in synthetic and real-world pest spread data.

Keywords:
Bayesian inferenceCox processGaussian processHMCMCMCpoint processspatial deformation

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Area of Science:

  • Spatial Statistics
  • Geostatistics
  • Computational Statistics

Background:

  • Traditional geostatistical methods often assume stationary spatial covariance.
  • There is a growing need for flexible models that account for nonstationarity in spatial point process applications.
  • Existing techniques for space-varying processes can be computationally intensive or lack data-driven adaptability.

Purpose of the Study:

  • To extend spatial Cox processes by incorporating data-driven spatial deformation to model nonstationarity.
  • To develop an efficient Bayesian inference framework using Hamiltonian Monte Carlo (HMC) methods.
  • To evaluate the proposed anisotropic nonstationary model against alternative formulations using synthetic and real-world data.

Main Methods:

  • A multivariate latent Gaussian process is used to drive the spatial deformation.
  • Markov Chain Monte Carlo (MCMC) methods, specifically Hamiltonian Monte Carlo (HMC), are employed for Bayesian inference.
  • The proposed spatial deformation model is compared with an anisotropic formulation using simulation studies and a case study.

Main Results:

  • The proposed spatial deformation method effectively captures nonstationary spatial covariance structures.
  • Hamiltonian Monte Carlo (HMC) significantly improved the computational efficiency of the Bayesian updating scheme compared to Metropolis-Hastings.
  • Studies with synthetic data and real-world pest spread data demonstrated the superiority of the proposed nonstationary anisotropic model.

Conclusions:

  • The proposed spatial deformation approach offers a powerful and flexible tool for modeling nonstationary spatial point processes.
  • The integration of data-driven deformation and efficient HMC inference enhances the applicability of complex spatial models.
  • The method shows significant advantages over traditional and alternative anisotropic models, particularly in ecological and agricultural applications.