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Bayesian semiparametric intensity estimation for inhomogeneous spatial point processes.

Yu Ryan Yue1, Ji Meng Loh

  • 1Baruch College, City University of New York, New York, New York 10010, USA. yu.yue@baruch.cuny.edu

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|December 24, 2010
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Summary
This summary is machine-generated.

We introduce a Bayesian method for spatial point process intensity estimation. This adaptive approach improves smoothing and covariate analysis for better data interpretation.

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Area of Science:

  • Spatial statistics
  • Statistical modeling
  • Computational statistics

Background:

  • Estimating intensity in spatial point processes is crucial for understanding spatial data.
  • Existing methods like parametric modeling and kernel smoothing have limitations in adaptivity and covariate analysis.

Purpose of the Study:

  • To propose a fully Bayesian semiparametric method for estimating the intensity of inhomogeneous spatial point processes.
  • To develop an adaptive approach that improves upon existing intensity estimation techniques.

Main Methods:

  • Convert intensity estimation to a Poisson regression setting by gridding data points.
  • Model log intensity semiparametrically using adaptive Gaussian Markov random fields.
  • Employ efficient Markov chain Monte Carlo (MCMC) simulation for inference.

Main Results:

  • The proposed method provides inference on covariate dependence.
  • It adaptively determines smoothing levels based on local data information.
  • Demonstrated effectiveness through simulation studies and a rainforest dataset application.

Conclusions:

  • The Bayesian semiparametric method offers a flexible and adaptive approach to spatial point process intensity estimation.
  • It outperforms traditional methods by incorporating adaptive smoothing and robust covariate analysis.