Geostatistical inference under preferential sampling

Peter J. Diggle, Raquel Menezes, Ting li Su

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)191-232
Number of pages42
JournalJournal of the Royal Statistical Society. Series C: Applied Statistics
Volume59
Issue number2
DOIs
StatePublished - Mar 2010

Keywords

  • Environmental monitoring
  • Geostatistics
  • Log-Gaussian Cox process
  • Marked point process
  • Monte Carlo inference
  • Preferential sampling

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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