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Geostatistical inference under preferential sampling
Author(s) -
Diggle Peter J.,
Menezes Raquel,
Su Tingli
Publication year - 2010
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2009.00701.x
Subject(s) - sampling (signal processing) , geostatistics , inference , statistics , monte carlo method , sampling design , data set , allowance (engineering) , computer science , mathematics , econometrics , data mining , spatial variability , artificial intelligence , engineering , population , demography , filter (signal processing) , sociology , computer vision , mechanical engineering
Summary. 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.