Linear Models for Spatial Data: Kriging
Just as data collected sequentially in time may be correlated, data collected at known locations in space may be correlated. For example, deposits of high-quality copper are more likely to occur near other high-quality deposits. The levels of lead contamination in the soil around a smelter are likely to be correlated. The prevalence of AIDS viewed geographically is correlated. There are innumerable situations in which data are collected at various locations in space and thus innumerable potential applications for methods of analysis for spatial data. One branch of statistics concerned with the analysis of such data is known as geostatistics. The practical application of geostatistics was developed in relative isolation from the mainstream of statistics. Not surprisingly, it uses some terminology that is unfamiliar to classically trained statisticians. David (1977) and Journel and Hüijbregts (1978) give details of the geostatistical approach using geostatistical terminology. Ripley (1981) takes a point of view that is probably more familiar to most statisticians. He uses ideas of prediction for stochastic processes that are closely related to time series methods. Cressie (1993) gives an excellent presentation of both the theory and application of statistics for spatial data. Stein (1999) gives an excellent account of the theory. Isaaks and Srivastava (1989) give a relatively elementary introduction; see also Cliff and Ord (1981). In this chapter, we present both traditional and geostatistical terminologies.
KeywordsCovariance Function Spatial Data Ordinary Kriging Nugget Effect Linear Unbiased Prediction
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