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Spatial Statistics and Geostatistics: Basic Concepts

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Encyclopedia of GIS

Historical Background

Statisticians have recognized impacts of correlated observations since the inception of their discipline. For example, in the early 1800s, while developing bivariate normal curve theory, Laplace acknowledged that between day variations in barometric pressure readings tend to be much greater than within day readings (Stigler 1986, p. 151). This thinking occurred during the emergence of multivariate statistics, being inspired in part by Lagrange’s contribution of the multivariate normal distribution in the early 1800s (Stigler 1986, ‘p. 118). Ultimately, statisticians developed both multivariate data analysis theory and its extension to correlated sample situations (e.g., the difference of correlated means, Hotelling (1931); the difference of correlated variances, Pitman (1939); the difference of correlated correlation coefficients, Dunn and Clark (1971)). Addressing variable correlation concerns spawned the addressing of observation correlation concerns in the...

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References

  • Chun Y, Griffith D (2015, forthcoming) Measuring spatial dependence. In: Richardson D, Castree N, Goodchild M, Kobayashi A, Liu W, Martson R (eds) International encyclopedia of geography. Wiley, New York

    Google Scholar 

  • Clayton D, Kaldor J (1987) Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics 43:671–681

    Article  Google Scholar 

  • Cliff A, Ord K (1973) Spatial autocorrelation. Pion, London

    Google Scholar 

  • Cliff A, Ord K (1975) The choice of a test for spatial autocorrelation In: Davis J, McCullagh M (eds) Display and analysis of spatial data. Wiley, New York, p 54–77

    Google Scholar 

  • Cressie N (1991) Statistics for spatial data. Wiley, New York

    MATH  Google Scholar 

  • Dunn O, Clark V (1971) Comparison of tests of the equality of dependent correlation coefficients. J Am Stat Assoc 66:904–908

    Article  Google Scholar 

  • Fisher R (1935) The design of experiments. Oliver and Boyd, Edinburgh

    Google Scholar 

  • Griffith D (1992) What is spatial autocorrelation? Reflections on the past 25 years of spatial statistics. L’Espace Géographique 21:265–280

    Article  Google Scholar 

  • Griffith D (1993) Advanced spatial statistics for analyzing and visualizing geo-referenced data. Int J Geogr Inf Syst 7:107–123

    Article  Google Scholar 

  • Griffith D (2003) Spatial autocorrelation and spatial filtering: gaining understanding through theory and scientific visualization. Springer, Berlin

    Book  Google Scholar 

  • Griffith D (2009) Methods: spatial autocorrelation. In: Kitchin R, Thrift N (eds) International encyclopedia of human geography. Elsevier, New York, p 396–402

    Chapter  Google Scholar 

  • Griffith D (2010) The Moran coefficient for non-normal data. J Stat Plan Inference 140:2980–2990

    Article  MathSciNet  MATH  Google Scholar 

  • Griffith D (2012) Spatial statistics: a quantitative geographer’s perspective. Spat Stat 1:3–15

    Article  Google Scholar 

  • Griffith D, Layne L (1997) Uncovering relationships between geo-statistical and spatial autoregressive models. In: The 1996 proceedings on the section on statistics and the environment, Chicago. American Statistical Association, pp. 91–96

    Google Scholar 

  • Grondona M, Cressie N (1991) Using spatial considerations in the analysis of experiments. Technometrics 33:381–392

    Article  MathSciNet  MATH  Google Scholar 

  • Hotelling H (1931) The generalization of student’s ratio. Ann Math Stat 2(3):360–378

    Article  MATH  Google Scholar 

  • Isserman A, Merrifield J (1982) The use of control groups in evaluating regional economic policy. Reg Sci Urban Econ 12:43–58

    Article  Google Scholar 

  • Krige D (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. J Chem Metall Min Soc S Afr 52:119–139

    Google Scholar 

  • Matheron G (1962) Traité de géostatistique appliquée. Editions Technip, Paris

    Google Scholar 

  • Neprash J (1934) Some problems in the correlation of spatially distributed variables. Proc Am Stat J New Ser 29(Suppl):167–168

    Google Scholar 

  • Paelinck J, Klaassen L (1979) Spatial econometrics. Saxon House, Farnborough

    Google Scholar 

  • Pitman E (1939) A note on normal correlation. Biometrika 31:9–12

    Article  MathSciNet  MATH  Google Scholar 

  • Stephan F (1934) Sampling errors and interpretations of social data ordered in time and space. Proc Am Stat J New Ser 29(Suppl):165–166

    Google Scholar 

  • Stigler S (1986) The history of statistics: the measurement of uncertainty before 1900. Harvard University Press, Cambridge

    MATH  Google Scholar 

  • Tsay R (2000) Time series and forecasting: brief history and future research. J Am Stat Assoc 95:638–643

    Article  Google Scholar 

  • Waller L, Gotway C (2004) Applied spatial statistics for public health data. Wiley, New York

    Book  MATH  Google Scholar 

  • Yule U (1926) Why do we sometimes get nonsense-correlations between time series? A study in sampling and the nature of time series. J R Stat Soc 89:1–69

    Article  MATH  Google Scholar 

  • Yule G (1927) On a method of investigating periodicities in disturbed series, with special reference to Wolfer’s sunspot numbers. Philos Trans R Soc A Math Phys Eng Sci 226:267–298

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Geospatial Information Sciences, School of Economic, Political and Policy Sciences, University of Texas at Dallas, 800 W. Campbell Rd, 75080-3021, Richardson, TX, USA

    Daniel Griffith

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  1. Daniel Griffith
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Correspondence to Daniel Griffith .

Editor information

Editors and Affiliations

  1. University of Minnesota, Minneapolis, MN, USA

    Shashi Shekhar

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

    Hui Xiong

  3. Department of Management Sciences, Tippie College of Business, University of Iowa, Iowa City, IA, USA

    Xun Zhou

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Griffith, D. (2017). Spatial Statistics and Geostatistics: Basic Concepts. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_1650

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