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Geostatistical inference under preferential sampling

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  • Peter J. Diggle
  • Raquel Menezes
  • Ting‐li Su

Abstract

Geostatistics involves the fitting of spatially continuous models to spatially discrete data. Preferential sampling arises when the process that determines the data locations and the process being modelled are stochastically dependent. Conventional geostatistical methods assume, if only implicitly, that sampling is non‐preferential. However, these methods are often used in situations where sampling is likely to be preferential. For example, in mineral exploration, samples may be concentrated in areas that are thought likely to yield high grade ore. We give a general expression for the likelihood function of preferentially sampled geostatistical data and describe how this can be evaluated approximately by using Monte Carlo methods. We present a model for preferential sampling and demonstrate through simulated examples that ignoring preferential sampling can lead to misleading inferences. We describe an application of the model to a set of biomonitoring data from Galicia, northern Spain, in which making allowance for preferential sampling materially changes the results of the analysis.

Suggested Citation

  • Peter J. Diggle & Raquel Menezes & Ting‐li Su, 2010. "Geostatistical inference under preferential sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 191-232, March.
  • Handle: RePEc:bla:jorssc:v:59:y:2010:i:2:p:191-232
    DOI: 10.1111/j.1467-9876.2009.00701.x
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    File URL: https://doi.org/10.1111/j.1467-9876.2009.00701.x
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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. Zhang, Shen & Liu, Xin & Tang, Jinjun & Cheng, Shaowu & Qi, Yong & Wang, Yinhai, 2018. "Spatio-temporal modeling of destination choice behavior through the Bayesian hierarchical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 537-551.
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    4. Simon N. Wood & Zheyuan Li & Gavin Shaddick & Nicole H. Augustin, 2017. "Generalized Additive Models for Gigadata: Modeling the U.K. Black Smoke Network Daily Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1199-1210, July.
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    7. Alexander Malinowski & Martin Schlather & Zhengjun Zhang, 2016. "Intrinsically weighted means and non-ergodic marked point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 1-24, February.
    8. Jane M. Lange & Rebecca A. Hubbard & Lurdes Y. T. Inoue & Vladimir N. Minin, 2015. "A joint model for multistate disease processes and random informative observation times, with applications to electronic medical records data," Biometrics, The International Biometric Society, vol. 71(1), pages 90-101, March.
    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. Alexander Malinowski & Martin Schlather & Zhengjun Zhang, 2016. "Intrinsically weighted means and non-ergodic marked point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 1-24, February.
    11. Benjamin M. Taylor & Ricardo Andrade‐Pacheco & Hugh J. W. Sturrock, 2018. "Continuous inference for aggregated point process data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1125-1150, October.
    12. Walter Dempsey & Peter McCullagh, 2018. "Survival models and health sequences," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 550-584, October.
    13. Duncan Lee & Claire Ferguson & E. Marian Scott, 2011. "Constructing representative air quality indicators with measures of uncertainty," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(1), pages 109-126, January.
    14. Martins, Thiago G. & Simpson, Daniel & Lindgren, Finn & Rue, Håvard, 2013. "Bayesian computing with INLA: New features," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 68-83.
    15. 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).
    16. Andriy Derkach & Jerald F. Lawless & Lei Sun, 2015. "Score tests for association under response-dependent sampling designs for expensive covariates," Biometrika, Biometrika Trust, vol. 102(4), pages 988-994.
    17. Bivand, Roger & Krivoruchko, Konstantin, 2018. "Big data sampling and spatial analysis: “which of the two ladles, of fig-wood or gold, is appropriate to the soup and the pot?”," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 87-91.

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