Encyclopedia of GIS

2008 Edition
| Editors: Shashi Shekhar, Hui Xiong

Hierarchical Spatial Models

  • Ali Arab
  • Mevin B. Hooten
  • Christopher K. Wikle
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-35973-1_564

Synonyms

Hierarchical dynamic spatio-temporal models; Geostatistical models; Hierarchies; Autoregressive models; Process model

Definition

A hierarchical spatial model is the product of conditional distributions for data conditioned on a spatial process and parameters, the spatial process conditioned on the parameters defining the spatial dependencies between process locations, and the parameters themselves.

Historical Background

Scientists across a wide range of disciplines have long recognized the importance of spatial dependencies in their data and the underlying process of interest. Initially due to computational limitations, they dealt with such dependencies by randomization and blocking rather than the explicit characterization of the dependencies in their models. Early developments in spatial modeling started in the 1950's and 1960's motivated by problems in mining engineering and meteorology [11], followed by the introduction of Markov random fields [2]. The application...

Keywords

Spatial Process Markov Random Field Geographically Weight Regression Areal Data Kriging Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Cressie, N.A.C.: Statistics for Spatial Data. Wiley & Sons, New York (1993)Google Scholar
  2. 2.
    Besag, J.: Spatial interactions and the statistical analysis of lattice systems (with discussion). J. Royal Stat. Soc., Series B 36, 192–236 (1974)MathSciNetMATHGoogle Scholar
  3. 3.
    Givens, G.H., Hoeting, J.A.: Computational Statistics. Wiley, New Jersey (2005)MATHGoogle Scholar
  4. 4.
    Lindley, D.V., Smith, A.F.M.: Bayes estimates for the linear model. J. Royal Stat. Soc., Series B 34, 1–41 (1972)MathSciNetMATHGoogle Scholar
  5. 5.
    Berliner, L.M.: Hierarchical Bayesian time series models. In: Hanson, K., Silver, R. (eds.) Maximum Entropy and Bayesian Methods, pp. 15–22. Kluwer Academic Publishers, Dordrecht (1996)CrossRefGoogle Scholar
  6. 6.
    Wikle, C.K., Berliner, L.M., Cressie, N.: Hierarchical Bayesian space-time models. J. Envr. Ecol. Stat. 5, 117–154 (1998)CrossRefGoogle Scholar
  7. 7.
    Banerjee, S., Carlin, B.P., Gelfand, A.E.: Hierarchical Modeling and Analysis for Spatial Data. Chapman & Hall/CRC, London, Boca Raton (2004)MATHGoogle Scholar
  8. 8.
    Diggle, P.J., Tawn, J.A., Moyeed, R.A.: Model-based geostatistics (with discussions). Appl. Stat. 47(3), 299–350 (1998)MathSciNetMATHGoogle Scholar
  9. 9.
    Wikle, C.K.: Hierarchical Bayesian models for predicting the spread of ecological processes. Ecol. 84, 1382–1394 (2003)CrossRefGoogle Scholar
  10. 10.
    Besag, J., York, J.C., Mollie, A.: Bayesian image restoration, with two applications in spatial statistics (with discussion) Ann. Inst. Stat. Math. 43, 1–59 (1991)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Whittle, P.: On Stationary Processes in the Plane. Biom., 41(3), 434–449 (1954)MathSciNetMATHGoogle Scholar
  12. 12.
    Cressie, N., Huang, H.-C.: Classes of nonseparable spatio-temporal stationary covariance functions. J. Am. Stat. Assoc. 94, 1330–1340 (1999)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Stein, M.L.: Space-time covariance functions. J. Am. Stat. Assoc. 100, 320–321 (2005)CrossRefGoogle Scholar
  14. 14.
    Waller, L.A., Xia, B.P., Gelfand, A.E.: Hierarchical spatio-temporal mapping of disease rates. J. Am. Stat. Assoc. 92, 607–617 (1997)MATHCrossRefGoogle Scholar
  15. 15.
    Wikle, C.K., Cressie, N.: A dimension-reduced approach to space-time Kalman filtering. Biom. 86(4), 815–829 (1999)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Ali Arab
    • 1
  • Mevin B. Hooten
    • 2
  • Christopher K. Wikle
    • 1
  1. 1.Department of StatisticsUniversity of Missouri-ColumbiaColumbiaUSA
  2. 2.Department of Mathematics and StatisticsUtah State UniversityLoganUSA