Environmental and Ecological Statistics

, Volume 22, Issue 2, pp 297–327 | Cite as

Bayesian hierarchical models for analysing spatial point-based data at a grid level: a comparison of approaches

  • Su Yun KangEmail author
  • James McGree
  • Kerrie Mengersen


Spatial data are now prevalent in a wide range of fields including environmental and health science. This has led to the development of a range of approaches for analysing patterns in these data. In this paper, we compare several Bayesian hierarchical models for analysing point-based data based on the discretization of the study region, resulting in grid-based spatial data. The approaches considered include two parametric models and a semiparametric model. We highlight the methodology and computation for each approach. Two simulation studies are undertaken to compare the performance of these models for various structures of simulated point-based data which resemble environmental data. A case study of a real dataset is also conducted to demonstrate a practical application of the modelling approaches. Goodness-of-fit statistics are computed to compare estimates of the intensity functions. The deviance information criterion is also considered as an alternative model evaluation criterion. The results suggest that the adaptive Gaussian Markov random field model performs well for highly sparse point-based data where there are large variations or clustering across the space; whereas the discretized log Gaussian Cox process produces good fit in dense and clustered point-based data. One should generally consider the nature and structure of the point-based data in order to choose the appropriate method in modelling a discretized spatial point-based data.


Gamma moving average model Grid-based spatial data  Integrated nested Laplace approximation Log Gaussian Cox process Markov chain Monte Carlo Semiparametric adaptive Gaussian Markov random field model 



The work has been supported by the Cooperative Research Centre for Spatial Information, whose activities are funded by the Australian Commonwealth’s Cooperative Research Centres Programme. Computational (and/or data visualization) resources and services used in part of this work were provided by the HPC and Research Support Unit, Queensland University of Technology, Brisbane, Australia. The authors would like to thank the reviewers and Adrian Baddeley for helpful suggestions and comments.

Supplementary material

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Su Yun Kang
    • 1
    • 2
    Email author
  • James McGree
    • 1
    • 2
  • Kerrie Mengersen
    • 1
    • 2
  1. 1.Mathematical Sciences SchoolQueensland University of TechnologyBrisbaneAustralia
  2. 2.CRC for Spatial InformationCarltonAustralia

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