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Convergence of posteriors for discretized log Gaussian Cox processes

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  • Waagepetersen, Rasmus

Abstract

In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations when the cell sizes of the discretization tends to zero. The effect of discretization is studied in a data example.

Suggested Citation

  • Waagepetersen, Rasmus, 2004. "Convergence of posteriors for discretized log Gaussian Cox processes," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 229-235, February.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:3:p:229-235
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    References listed on IDEAS

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    1. Anders Brix & Peter J. Diggle, 2001. "Spatiotemporal prediction for log‐Gaussian Cox processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 823-841.
    2. Anders Brix & Jesper Moller, 2001. "Space‐time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 471-488, September.
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    1. D. Simpson & J. B. Illian & F. Lindgren & S. H. Sørbye & H. Rue, 2016. "Going off grid: computationally efficient inference for log-Gaussian Cox processes," Biometrika, Biometrika Trust, vol. 103(1), pages 49-70.
    2. Rasmus Waagepetersen & Yongtao Guan, 2009. "Two‐step estimation for inhomogeneous spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 685-702, June.

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