International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

Model-Based Geostatistics

  • Hannes Kazianka
  • Jürgen Pilz
Reference work entry

Stochastic Models for Spatial Data

Diggle and Ribeiro (2007) and Mase (2010) describe geostatistics as a branch of spatial statistics that deals with statistical methods for the analysis of spatially referenced data with the following properties. Firstly, values Yi, i = 1, …, n, are observed at a discrete set of sampling locations xi within some spatial region \(\mathcal{S} \, \subset \mathbb{R}^d,d\geq 2\)

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References and Further Reading

  1. De Oliveira V, Kedem B, Short D (1997) Bayesian prediction of transformed Gaussian fields. J Am Stat Assoc 92:1422–1433zbMATHGoogle Scholar
  2. Diggle P, Ribeiro P (2007) Model-based geostatistics. Springer, New YorkzbMATHGoogle Scholar
  3. Sempi C (2010) Copulas. (this volume)Google Scholar
  4. Kazianka H, Pilz J (2009) Copula-based geostatistical modeling of continuous and discrete data including covariates. Stoch Env Res Risk Assess, doi: 10.1007/s00477-009-0353-8Google Scholar
  5. Kitanidis P (1986) Parameter uncertainty in estimation of spatial function: Bayesian analysis. Water Resour Res 22:499–507Google Scholar
  6. Mase S (2010) Geostatistics and kriging predictors. (this volume)Google Scholar
  7. McCullagh P, Nelder J (1989) Generalized linear models. Chapman & Hall/CRC, Boca RatonzbMATHGoogle Scholar
  8. Omre H (1987) Bayesian kriging – merging observations and qualified guesses in kriging. Math Geol 19:25–39MathSciNetGoogle Scholar
  9. Robert C, Casella G (2004) Monte Carlo statistical methods. Springer, New YorkzbMATHGoogle Scholar
  10. Schabenberger O, Gotway C (2005) Statistical methods for spatial data analysis. Chapman & Hall/CRC, Boca RatonzbMATHGoogle Scholar
  11. Stein M (1999) Interpolation of spatial data. Springer, New YorkzbMATHGoogle Scholar
  12. Yaglom A (1987) Correlation theory of stationary and related random functions. Springer, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hannes Kazianka
    • 1
  • Jürgen Pilz
    • 2
  1. 1.University of TechnologyViennaAustria
  2. 2.University of KlagenfurtKlagenfurtAustria