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Careful prior specification avoids incautious inference for log‐Gaussian Cox point processes

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  • Sigrunn H. S⊘rbye
  • Janine B. Illian
  • Daniel P. Simpson
  • David Burslem
  • Håvard Rue

Abstract

Hyperprior specifications for random fields in spatial point process modelling can have a major influence on the results. In fitting log‐Gaussian Cox processes to rainforest tree species, we consider a reparameterized model combining a spatially structured and an unstructured random field into a single component. This component has one hyperparameter accounting for marginal variance, whereas an additional hyperparameter governs the fraction of the variance that is explained by the spatially structured effect. This facilitates interpretation of the hyperparameters, and significance of covariates is studied for a range of hyperprior specifications. Appropriate scaling makes the analysis invariant to grid resolution.

Suggested Citation

  • Sigrunn H. S⊘rbye & Janine B. Illian & Daniel P. Simpson & David Burslem & Håvard Rue, 2019. "Careful prior specification avoids incautious inference for log‐Gaussian Cox point processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(3), pages 543-564, April.
    • Handle: RePEc:bla:jorssc:v:68:y:2019:i:3:p:543-564
    DOI: 10.1111/rssc.12321
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    1. Williamson, Laura D. & Scott, Beth E. & Laxton, Megan & Illian, Janine B. & Todd, Victoria L.G. & Miller, Peter I. & Brookes, Kate L., 2022. "Comparing distribution of harbour porpoise using generalized additive models and hierarchical Bayesian models with integrated nested laplace approximation," Ecological Modelling, Elsevier, vol. 470(C).
    2. Chen, Jiaxun & Micheas, Athanasios C. & Holan, Scott H., 2022. "Hierarchical Bayesian modeling of spatio-temporal area-interaction processes," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).

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