Mathematical Geology

, Volume 22, Issue 3, pp 239–252 | Cite as

The origins of kriging

  • Noel Cressie


In this article, kriging is equated with spatial optimal linear prediction, where the unknown random-process mean is estimated with the best linear unbiased estimator. This allows early appearances of (spatial) prediction techniques to be assessed in terms of how close they came to kriging.

Key words

blue blup covariance function geodesy homogeneous structure function meteorology mining optimum interpolation spatial blup statistics variogram 


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  1. Cressie, N., 1991, Statistics for spatial data: Wiley, New York (forthcoming).Google Scholar
  2. Fairfield Smith, H., 1936, A discriminant function for plant selection: Annals of Eugenics, v. 7, p. 240–250.Google Scholar
  3. Gandin, L. S., 1963, Objective analysis of meteorological fields: Gidrometeorologicheskoe Izdatel'stvo (GIMIZ), Leningrad (translated by Israel Program for Scientific Translations, Jerusalem, 1965, 238 pp.).Google Scholar
  4. Gauss, C. F., 1809, Theoria motus corporum celestium: Perthes et Besser, Hamburg (tranlslated as Theory of motion of the heavenly bodies moving about the sun in conic sections, trans. C. H. Davis: Little, Brown, Boston, 1857).Google Scholar
  5. Goldberg, A. S., 1962, Best linear unbiased prediction in the generalized linear regression model: J. Am. Stat. Assoc., v. 57, p. 369–375.Google Scholar
  6. Hazel, L. N., 1943. The genetic basis for constructing selection indexes: Genetics, v. 28, p. 476–490.Google Scholar
  7. Hemyari, P., and Nofziger, D. L., 1987, Analytical solution for punctual kriging in one dimension: Soil Sci. Soc. Am. J., 51, p. 268–269.Google Scholar
  8. Henderson, C. R., 1963, Selection index and expected genetic advance,in Statistical genetics and plant breeding, W. D. Hanson and H. F. Robinson (Eds.): National Research Council Publication 982, National Academy of Sciences, Washington, D.C., p. 141–163.Google Scholar
  9. Journel, A. G., and Huijbregts, C. J., 1978, Mining geostatics: Academic Press, London, 600 pp.Google Scholar
  10. Kolmogorov, A. N., 1941a, Interpolation and extrapolation of stationary random sequences: Izvestiia Akademii Nauk SSR, Seriia Matematicheskaia, v. 5, p. 3–14 (translation, Memo RM-3090-PR, Rand Corporation, Santa Monica, California, 1962, 14 pp.).Google Scholar
  11. Kolmogorov, A. N., 1941b, The local structure of turbulence in an incompressible fluid at very large Reynolds numbers: Doklady Akademii Nauk SSR, v. 30, p. 301–305 (reprinted in Turbulence: classic papers of statistical theory, S. K. Friedlander and L. Topping (Ed.): Interscience Publishers, New York, 1961, p. 151–155).Google Scholar
  12. Krige, D. G., 1951, A statistical approach to some basic mine valuation problems on the Witwatersrand: J. Chem. Metal. Min. Soc. South Africa, v. 52, p. 119–139.Google Scholar
  13. Krige, D. G., 1962a, Effective pay limits for selective mining: J. South Africa Inst. Min. Metal., v. 62, p. 345–363.Google Scholar
  14. Krige, D. G., 1962b, Economic aspects of stoping through unpayable ore: J. South African Inst. Min. Metal., v. 62, p. 364–374.Google Scholar
  15. Krige, D. G., 1966, Two-dimensional weighted moving average trend surfaces for ore valuation,in Symposium on mathematical statistics and computer applications in ore valuation: Johannesberg, South Africa, 1966. Special issue of J. South African Inst. Min. Metal., p. 13–79.Google Scholar
  16. Krige, D. G., 1978, Lognormal-de Wijsian geostatistics for ore evaluation: South African Institute of Mining and Metallurgy Monograph Series, Johannesburg, 50 pp.Google Scholar
  17. Krige, D. G., and Ueckermann, H. J., 1963, Value contours and improved regression techniques for ore reserve valuations: J. South African Inst. Min. Metal., v. 63, p. 429–452.Google Scholar
  18. Legendre, A. M., 1805, Nouvelles méthodes pour la détermination des orbites des cométes: Courcier, Paris, 80 pp.Google Scholar
  19. Matern, B., 1960, Spatial variation: Meddelanden fran Statens Skogsforskningsinstitute, v. 49, 144 pp.Google Scholar
  20. Matheron, G., 1962, Traité de geostatisque appliquée, vol. I: Memoires du Bureau de Recherches Géologiques et Miniéres, no. 14, Editions Technip, Paris, 333 pp.Google Scholar
  21. Matheron, G., 1963a, Traité de geostatistique appliquée, vol. II, Le krigeage: Memoires du Bureau de Recherches Géologiques et Miniéres, no. 24, Editions Bureau de Recherche Géologiques et Miniéres, Paris, 171, pp.Google Scholar
  22. Matheron, G., 1963b, Principles of geostatistics: Economic Geol., v. 58, p. 1246–1266.Google Scholar
  23. Matheron, G., 1967, Kriging or polynomial interpolation procedures?: Trans. Canad. Inst. Min. Metal., v. 70, p. 240–244.Google Scholar
  24. Moritz, H., 1963, Statistische methoden in der gravimetrischen geodasie: Zeitschrift fur Vermessungswesen, v. 88, p. 409–416.Google Scholar
  25. Ord, J. K., 1983, Kriging, entry,in Encyclopedia of statistical sciences, vol. 4, S. Kotz and N. Johnson (Eds.): Wiley, New York, p. 411–413.Google Scholar
  26. Stigler, S. M., 1980, Stigler's law of eponymy: Trans. New York Acad. Sci. Series 2, v. 39 (Merton Festschrift Vol., ed. by T. Gieryn), p. 147–158.Google Scholar
  27. Thompson, P. D., 1956, Optimum smoothing of two-dimensional fields: Tellus, v. 8, p. 384–393.Google Scholar
  28. Whitten, E. H. T., 1966, The general linear equation in prediction of gold content in Witwatersrand rocks, South Africa,in Symposium on mathematical statistics and computer applications in ore valuation: Johannesberg, South Africa, 1966; special issue of J. South African Inst. Min. Metal., p. 124–147.Google Scholar
  29. Whittle, P., 1963, Prediction and regulation by linear least-square methods: van Nostrand, Princeton, 141 pp.Google Scholar
  30. Wiener, N., 1949, Extrapolation, interpolation and smoothing of stationary time series: MIT Press, Cambridge, Massachusetts, 158 pp.Google Scholar
  31. Wold, H., 1938, A. study in the analysis of stationary time series: Almqvist and Wiksells, Uppsala, 211 pp.Google Scholar
  32. Yaglom, A. M., 1957, Some classes of random fields inn-dimensional space, related to stationary random processes: Theory Prob. Appl., v. 2, p. 273–320.Google Scholar
  33. Yaglom, A. M., 1962, An introduction to the theory of stationary random functions: Prentice-Hall (as of 1973, published by Dover, New York, 235 pp.).Google Scholar

Copyright information

© International Association for Mathematical Geology 1990

Authors and Affiliations

  • Noel Cressie
    • 1
  1. 1.Department of StatisticsIowa State UniversityAmes

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