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Bayesian geostatistical modelling with informative sampling locations

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  • D. Pati
  • B. J. Reich
  • D. B. Dunson

Abstract

We consider geostatistical models that allow the locations at which data are collected to be informative about the outcomes. A Bayesian approach is proposed, which models the locations using a log Gaussian Cox process, while modelling the outcomes conditionally on the locations as Gaussian with a Gaussian process spatial random effect and adjustment for the location intensity process. We prove posterior propriety under an improper prior on the parameter controlling the degree of informative sampling, demonstrating that the data are informative. In addition, we show that the density of the locations and mean function of the outcome process can be estimated consistently under mild assumptions. The methods show significant evidence of informative sampling when applied to ozone data over Eastern U.S.A. Copyright 2011, Oxford University Press.

Suggested Citation

  • D. Pati & B. J. Reich & D. B. Dunson, 2011. "Bayesian geostatistical modelling with informative sampling locations," Biometrika, Biometrika Trust, vol. 98(1), pages 35-48.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:1:p:35-48
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    File URL: http://hdl.handle.net/10.1093/biomet/asq067
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    Cited by:

    1. Nathan A. Ryder & Joshua P. Keller, 2023. "Spatiotemporal Exposure Prediction with Penalized Regression," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(2), pages 260-278, June.
    2. Baveye, Philippe C. & Laba, Magdeline, 2015. "Moving away from the geostatistical lamppost: Why, where, and how does the spatial heterogeneity of soils matter?," Ecological Modelling, Elsevier, vol. 298(C), pages 24-38.
    3. Lucia Paci & Alan E. Gelfand & and María Asunción Beamonte & Pilar Gargallo & Manuel Salvador, 2020. "Spatial hedonic modelling adjusted for preferential sampling," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 169-192, January.
    4. Erin M. Schliep & Christopher K. Wikle & Ranadeep Daw, 2023. "Correcting for informative sampling in spatial covariance estimation and kriging predictions," Journal of Geographical Systems, Springer, vol. 25(4), pages 587-613, October.
    5. Brian J. Reich & Shu Yang & Yawen Guan & Andrew B. Giffin & Matthew J. Miller & Ana Rappold, 2021. "A Review of Spatial Causal Inference Methods for Environmental and Epidemiological Applications," International Statistical Review, International Statistical Institute, vol. 89(3), pages 605-634, December.
    6. Brian Conroy & Lance A. Waller & Ian D. Buller & Gregory M. Hacker & James R. Tucker & Mark G. Novak, 2023. "A Shared Latent Process Model to Correct for Preferential Sampling in Disease Surveillance Systems," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 483-501, September.
    7. Samira Zahmatkesh & Mohsen Mohammadzadeh, 2021. "Bayesian prediction of spatial data with non-ignorable missingness," Statistical Papers, Springer, vol. 62(5), pages 2247-2268, October.
    8. Aubry, Philippe & Francesiaz, Charlotte & Guillemain, Matthieu, 2024. "On the impact of preferential sampling on ecological status and trend assessment," Ecological Modelling, Elsevier, vol. 492(C).
    9. Brian J. Reich & Howard H. Chang & Kristen M. Foley, 2014. "A spectral method for spatial downscaling," Biometrics, The International Biometric Society, vol. 70(4), pages 932-942, December.
    10. Johnston, Alison & Moran, Nick & Musgrove, Andy & Fink, Daniel & Baillie, Stephen R., 2020. "Estimating species distributions from spatially biased citizen science data," Ecological Modelling, Elsevier, vol. 422(C).

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