IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v59y2010i2p191-232.html
   My bibliography  Save this article

Geostatistical inference under preferential sampling

Author

Listed:
  • 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. Copyright (c) 2010 Royal Statistical Society.

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.
  • Handle: RePEc:bla:jorssc:v:59:y:2010:i:2:p:191-232
    as

    Download full text from publisher

    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9876.2009.00701.x
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts & Paul Fearnhead, 2006. "Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 333-382.
    2. Roula Tsonaka & Geert Verbeke & Emmanuel Lesaffre, 2009. "A Semi-Parametric Shared Parameter Model to Handle Nonmonotone Nonignorable Missingness," Biometrics, The International Biometric Society, vol. 65(1), pages 81-87, March.
    3. Caroline Beunckens & Geert Molenberghs & Geert Verbeke & Craig Mallinckrodt, 2008. "A Latent-Class Mixture Model for Incomplete Longitudinal Gaussian Data," Biometrics, The International Biometric Society, vol. 64(1), pages 96-105, March.
    4. Michael L. Stein, 2005. "Space-Time Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 310-321, March.
    5. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    6. Gelfand, Alan E. & Kottas, Athanasios & MacEachern, Steven N., 2005. "Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1021-1035, September.
    7. Haiqun Lin & Daniel O. Scharfstein & Robert A. Rosenheck, 2004. "Analysis of longitudinal data with irregular, outcome-dependent follow-up," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 791-813.
    8. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
    9. Paul Fearnhead & Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Particle filters for partially observed diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 755-777.
    10. Xiao Song & Marie Davidian & Anastasios A. Tsiatis, 2002. "A Semiparametric Likelihood Approach to Joint Modeling of Longitudinal and Time-to-Event Data," Biometrics, The International Biometric Society, vol. 58(4), pages 742-753, December.
    11. Ryu, Duchwan & Sinha, Debajyoti & Mallick, Bani & Lipsitz, Stuart R. & Lipshultz, Steven E., 2007. "Longitudinal Studies With Outcome-Dependent Follow-up: Models and Bayesian Regression," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 952-961, September.
    12. Stuart R. Lipsitz & Garrett M. Fitzmaurice & Joseph G. Ibrahim & Richard Gelber & Steven Lipshultz, 2002. "Parameter Estimation in Longitudinal Studies with Outcome-Dependent Follow-Up," Biometrics, The International Biometric Society, vol. 58(3), pages 621-630, September.
    13. Martin Schlather & Paulo J. Ribeiro & Peter J. Diggle, 2004. "Detecting dependence between marks and locations of marked point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 79-93.
    14. Peter McCullagh, 2008. "Sampling bias and logistic models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 643-677.
    15. Ho, Lai Ping & Stoyan, D., 2008. "Modelling marked point patterns by intensity-marked Cox processes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1194-1199, August.
    16. Julian Besag & Debashis Mondal, 2005. "First-order intrinsic autoregressions and the de Wijs process," Biometrika, Biometrika Trust, vol. 92(4), pages 909-920, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:spr:stabio:v:9:y:2017:i:2:d:10.1007_s12561-016-9150-3 is not listed on IDEAS
    2. Yi Liu & Gavin Shaddick & James V. Zidek, 0. "Incorporating High-Dimensional Exposure Modelling into Studies of Air Pollution and Health," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 0, pages 1-23.
    3. 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.
    4. Martins, Thiago G. & Simpson, Daniel & Lindgren, Finn & Rue, HÃ¥vard, 2013. "Bayesian computing with INLA: New features," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 68-83.
    5. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssc:v:59:y:2010:i:2:p:191-232. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/rssssea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.