GEOSTATISTICAL INFERENCE UNDER PREFERENTIAL SAMPLING
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Abstract:
Geostatistics involves the fitting of spatially continuous models to spatially discrete data (Chil`es and Delfiner, 1999). 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 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 using Monte Carlo methods. We present a model for preferential sampling, and demonstrate through simulated examples that ignoring preferential sampling can lead to seriously misleading inferences. We describe an application of the model to a set of bio-monitoring data from Galicia, northern Spain, in which making allowance for preferential sampling materially changes the inferences.
Subject Area:
Statistical Theory and Methods
Suggested Citation:
Peter J. Diggle, Raquel Menezes, and Ting-li Su, "GEOSTATISTICAL INFERENCE UNDER PREFERENTIAL SAMPLING" (January 2008). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 162.
http://www.bepress.com/jhubiostat/paper162