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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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