An Introduction to Model-Based Geostatistics (original) (raw)

References

• Adler, R. J. (1981). The Geometry of Random Fields, Wiley, New York.
  MATH Google Scholar
• Berger, J. O., De Oliveira, V. and Sansb, B. (2001). Objective Bayesian analysis of spatially correlated data, Journal of the American Statistical Association 96: 1361–1374.
  Article MathSciNet MATH Google Scholar
• Besag, J., York, J. and Mollié, A. (1991). Bayesian image restoration, with two applications in spatial statistics (with discussion), Annals of the Institute of Statistical Mathematics 43: 1–59.
  Google Scholar
• Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association 88: 9–25.
  Google Scholar
• Brix, A. and Diggle, P. J. (2001). Spatio-temporal prediction for log-Gaussian Cox processes, Journal of the Royal Statistical Society, Series B 63: 823–841.
  Google Scholar
• Brown, P. E., Diggle, P. J., Lord, M. E. and Young, P. C. (2001). Space-time calibration of radar rainfall data, Applied Statistics 50: 221–241.
  Google Scholar
• Brown, P. E., Khrensen, K. F., Roberts, G. O. and Tonellato, S. (2000). Blur-generated non-separable space-time models, Journal of the Royal Statistical Society, Series B 62: 847–860.
  Google Scholar
• Brown, P. J., Le, N. D. and Zidek, J. V. (1994). Multivariate spatial interpolation and exposure to air polutants, Canadian Journal of Statistics 22: 489–509.
  Article MathSciNet MATH Google Scholar
• Chilés, J. P. and Delfiner, P. (1999). Geostatistics; Modeling Spatial Uncertainty, Wiley, New York.
  Book MATH Google Scholar
• Christensen, O. F., Diggle, P. J. and Ribeiro Jr, P. J. (2001). Analysing positive-valued spatial data: the transformed Gaussian model, in P. Monestiez, D. Allard and R. Froidevaux (eds), GeoENV III–Geostatistics for Environmental Applications, Vol. 11 of Quantitative Geology and Geostatistics, Kluwer, Dordrecht, pp. 287–298.
  Google Scholar
• Christensen, O. F., Moller, J. and Waagepetersen, R. (2001). Geometric ergodicity of Metropolis Hastings algorithms for conditional simulation in generalised linear mixed models, Methodology and Computing in Applied Probability 3: 309–327.
  Google Scholar
• Christensen, O. F. and Waagepetersen, R. P. (2002). Bayesian prediction of spatial count data using generalized linear mixed models, Biometrics 58: 280–286.
  Google Scholar
• Cramer, H. and Leadbetter, M. R. (1967). Stationary and Related Processes, Wiley, New York.
  MATH Google Scholar
• Cressie, N. (1993). Statistics for Spatial Data — revised edition, Wiley, New York.
  Google Scholar
• De Oliveira, V. (2000). Bayesian prediction of clipped Gaussian random fields, Computational Statistics and Data Analysis 34: 299–314.
  Article MATH Google Scholar
• De Oliveira, V. and Ecker, M. D. (2002). Bayesian hot spot detection in the presence of a spatial trend: application to total nitrogen concentration in the Chesapeake Bay, Environmetrics 13: 85–101.
  Google Scholar
• De Oliveira, V., Kedem, B. and Short, D. A. (1997). Bayesian prediction of transformed Gaussian random fields, Journal of the American Statistical Association 92: 1422–1433.
  MathSciNet MATH Google Scholar
• Diggle, P. J., Harper, L. and Simon, S. (1997). Geostatistical analysis of residual contamination from nuclear weapons testing, in V. Barnett and F. Turkman (eds), Statistics for the Environment 3: Pollution Assesment and Control, Wiley, Chichester, pp. 89–107.
  Google Scholar
• Diggle, P. J. and Ribeiro Jr, P. J. (2002). Bayesian inference in Gaussian model based geostatistics, Geographical and Environmental Modelling 6. To appear.
  Google Scholar
• Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998). Model based geostatistics (with discussion), Applied Statistics 47: 299–350.
  MathSciNet MATH Google Scholar
• Geyer, C. J. (1992). Practical Markov chain Monte Carlo (with discussion), Statistical Science 7: 473–511.
  Article Google Scholar
• Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation, Oxford University Press, New York.
  Google Scholar
• Gotway, C. A. and Stroup, W. W. (1997). A generalized linear model approach to spatial data analysis and prediction, Journal of Agricultural, Biological and Environmental Statistics 2: 157–178.
  Article MathSciNet Google Scholar
• Handcock, M. S. and Stein, M. L. (1993). A Bayesian analysis of kriging, Technometrics 35: 403–410.
  Article Google Scholar
• Handcock, M. S. and Wallis, J. R. (1994). An approach to statistical spatial-temporal modeling of meteorological fields, Journal of the American Statistical Association 89: 368–390.
  Article MathSciNet MATH Google Scholar
• Heagerty, P. J. and Lele, S. R. (1998). A composite likelihood approach to binary spatial data, Journal of the American Statistical Association 93: 1099–1111.
  Article MathSciNet MATH Google Scholar
• Ihaka, R. and Gentleman, R. (1996). R: A language for data analysis and graphics, Journal of Computatioanl and Graphical Statistics 5: 299–314.
  Google Scholar
• Journel, A. G. and Huijbregts, C. J. (1978). Mining Geostatistics, Academic Press, London.
  Google Scholar
• Kent, J. T. (1989). Continuity properties of random fields, Annals of Probability 17: 1432–1440.
  Article MathSciNet MATH Google Scholar
• Kitanidis, P. K. (1983). Statistical estimation of polynomial generalized covariance functions and hydrological applications., Water Resources Research 22: 499–507.
  Article Google Scholar
• Kitanidis, P. K. (1986). Parameter uncertainty in estimation of spatial functions: Bayesian analysis, Water Resources Research 22: 499–507.
  Article Google Scholar
• Krige, D. G. (1951). A statistical approach to some basic mine valuation problems on the Witwatersrand, Journal of the Chemical, Metallurgical and Mining Society of South Africa 52: 119–139.
  Google Scholar
• Le, N. D., Sun, W. and Zidek, J. V. (1997). Bayesian multivariate spatial interpolation with data missing by design, Journal of the Royal Statistical Society, Series B 59: 501–510.
  Article MathSciNet MATH Google Scholar
• Le, N. D. and Zidek, J. V. (1992). Interpolation with uncertain covariances: a Bayesian alternative to kriging, Journal of Multivariate Analysis 43: 351–374.
  Google Scholar
• Mardia, K. V. and Watkins, A. J. (1989). On multimodality of the likelihood in the spatial linear model, Biometrika 76: 289–296.
  Article MathSciNet MATH Google Scholar
• Matérn, B. (1960). Spatial Variation. Meddelanden fran Statens Skogforskningsinstitut, Band 49, No. 5.
  Google Scholar
• McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, second edn, Chapman and Hall, London.
  MATH Google Scholar
• Natarajan, R. and Kass, R. E. (2000). Bayesian methods for generalized linear mixed models, Journal of the American Statistical Association 95: 227–237.
  Google Scholar
• O’Hagan, A. (1994). Bayesian Inference,Vol. 2b of Kendall’s Advanced Theory of Statistics,Edward Arnold.
  Google Scholar
• Omre, H. and Halvorsen, K. B. (1989). The Bayesian bridge between simple and universal kriging, Mathematical Geology 21: 767–786.
  Article MathSciNet MATH Google Scholar
• Patterson, H. D. and Thompson, R. (1971). Recovery of inter-block infor- mation when block sizes are unequal, Biometrika 58: 545–554.
  Google Scholar
• Ribeiro Jr, P. J. and Diggle, P. J. (1999). Bayesian inference in Gaussian model-based geostatistics, Tech. Report ST-99–09,Lancaster University.
  Google Scholar
• Ribeiro Jr, P. J. and Diggle, P. J. (2001). geoR: a package for geostatistical analysis, R News 1/2: 15–18. Available from: http://www.rproject.org/doc/Rnews.
  Google Scholar
• Ripley, B. D. (1981). Spatial Statistics, Chapman and Hall, New York.
  Book MATH Google Scholar
• Sampson, P. D. and Guttorp, P. (1992). Nonparametric estimation of non-stationary spatial covariance structure, Journal of the American Statistical Association 87: 108–119.
  Article Google Scholar
• Schlather, M. (2001). On the second-order characteristics of marked point processes, Bernoulli 7: 99–117.
  Article MathSciNet MATH Google Scholar
• Stein, M. L. (1999). Interpolation of Spatial Data: Some Theory for Kriging, Springer Verlag, New York.
  Book MATH Google Scholar
• Wälder, O. and Stoyan, D. (1996). On variograms in point process statistics, Biometrical Journal 38: 895–905.
  Article MATH Google Scholar
• Wälder, O. and Stoyan, D. (1998). On variograms in point process statistics: Erratum, Biometrical Journal 40: 109.
  Google Scholar
• Warnes, J. J. and Ripley, B. D. (1987). Problems with likelihood estimation of covariance functions of spatial Gaussian processes, Biometrika 74: 640–642.
  Article MathSciNet MATH Google Scholar
• Whittle, P. (1954). On stationary processes in the plane, Biometrika 41: 434–449.
  MathSciNet MATH Google Scholar
• Whittle, P. (1962). Topographic correlation, power-law covariance functions, and diffusion, Biometrika 49: 305–314.
  MathSciNet MATH Google Scholar
• Whittle, P. (1963). Stochastic processes in several dimensions, Bulletin of the International Statistical Institute 40: 974–994.
  MathSciNet Google Scholar
• Wikle, C. K. and Cressie, N. (1999). A dimension-reduced approach to space-time Kalman filtering, Biometrika 86: 815–829.
  Article MathSciNet MATH Google Scholar
• Zhang, H. (2002). On estimation and prediction for spatial generalised linear mixed models, Biometrics 58: 129–136.
  Article MathSciNet MATH Google Scholar
• Zidek, J. V., Sun, W. and Le, N. D. (2000). Designing and integrating composite networks for monitoring multivariate Gaussian pollution field, Applied Statistics 49: 63–79.
  MathSciNet MATH Google Scholar
• Zimmerman, D. L. (1989). Computationally efficient restricted maximum likelihood estimation of generalized covariance functions, Mathematical Geology 21: 655–672.
  Article MathSciNet Google Scholar

Download references