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Kriging

  • Reference work entry
Encyclopedia of GIS

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Synonyms

Optimum interpolation; Optimal prediction; Variogram; Spatial dependence

Definition and Historical Background

Kriging is a spatial interpolation technique which has applications in spatial prediction and automatic contouring. It was developed by Georges Matheron, who named the technique after D.J. Krige, a South African mining engineer who did some of the early work on the topic.

Scientific Fundamentals

In a standard statistical analysis, all of the data are assumed to come from the same distribution, and can thus be used to estimate the parameters of this distribution. The idea of repeat sampling also plays an important role. For example, the reason that sample estimates are random variables is that different samples will produce different estimates of the same parameter. In spatial statistics, a somewhat different paradigm is required. In a spatial setting, often the very act of collecting the sample destroys it, so that repeat sampling is not an option. For example, if...

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Notes

  1. 1.

    In general, a location will be identified by a vector of coordinates. However, here s is used as a label rather than a vector of coordinates. Locations that are h units away from s are denoted by (s+h). Thus, both s and h are treated as scalars rather than vectors (the standard treatment in the literature is to treat them as vectors).

  2. 2.

    This section draws heavily from Ripley, chapter 4.

  3. 3.

    The material in this and the next section draw heavily on Cressie, chapter 3.

  4. 4.

    In a model designed to predict housing prices, Dubin hypothesizes that the mean is a function of housing characteristics as well as the coordinates.

Recommended Reading

  1. Dubin, R.A.: Predicting House Prices Using Multiple Listings Data. Journal of Real Estate Finance and Economics 17(1), 35–60 (1998)

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  2. Cressie, N.: Statistics for Spatial Data. Wiley and Sons, Inc., New York (1991)

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  3. Cressie, N., Read, T.R.C.: Do Sudden Infant Deaths Come in Clusters?. Statistics and Decisions, Supplement Issue 2(3), 333–349 (1985)

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  4. Istok, J.D., Cooper, R.M.: Geostatistics Applied to Groundwater Pollution. Journal of Environmental Engineering 114, 915–928 (1988)

    Article  Google Scholar 

  5. Olea, R.: Optimum Mapping Techniques. Kansas Geological Survey, Lawrence, Kansas (1975)

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  6. Ord, J.K., Rees, M.: Spatial Processes: Recent Developments with Applications to Hydrology. In: Lloyd, E.H., et. al (eds.) The Mathematics of Hydrology and Water Resources. Academic Press, New York (1979)

    Google Scholar 

  7. Ripley, B.: Spatial Statistics. Wiley and Sons, Inc., New York (1981)

    Book  MATH  Google Scholar 

  8. Samra, J.S., Gill, H.S., Bhatia, V.K.: Spatial Stochastic Modeling of Growth and Forest Resource Evaluation. Forest Science 35, 663–676 (1989)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Economics, Weatherhead School of Management, Case Western Reserve University, Cleveland, OH, USA

    Robin Dubin

Authors
  1. Robin Dubin
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Shashi Shekhar (McKnight Distinguished University Professor) (McKnight Distinguished University Professor)

  2. Management Science and Information Systems Department, Rutgers Business School Newark and New Brunswick Rutgers, the State University of New Jersey, Newark, NJ, 07102, USA

    Hui Xiong (Assistant Professor) (Assistant Professor)

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© 2008 Springer-Verlag

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Dubin, R. (2008). Kriging. In: Shekhar, S., Xiong, H. (eds) Encyclopedia of GIS. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35973-1_675

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