Bayesian Semiparametric Intensity Estimation for Inhomogeneous Spatial Point Processes

Yu Ryan Yue, Ji Meng Loh

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this work we propose a fully Bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process. The basic idea is to first convert intensity estimation into a Poisson regression setting via binning data points on a regular grid, and then model the log intensity semiparametrically using an adaptive version of Gaussian Markov random fields to smooth the corresponding counts. The inference is carried by an efficient Markov chain Monte Carlo simulation algorithm. Compared to existing methods for intensity estimation, for example, parametric modeling and kernel smoothing, the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates, but also uses information from the data to adaptively determine the amount of smoothing at the local level. The effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset.

Original languageEnglish (US)
Pages (from-to)937-946
Number of pages10
JournalBiometrics
Volume67
Issue number3
DOIs
StatePublished - Sep 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Keywords

  • Adaptive spatial smoothing
  • Gaussian Markov random fields
  • Gibbs sampling
  • Intensity estimation
  • Spatial point process

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