Bayesian Variogram Modeling for an Isotropic Spatial Process

Journal of Agricultural, Biological, and Environmental Statistics

Volumn 2, Issue 4, 1997, Pages 347-369

  Ecker, Mark D ^a   Gelfand, Alan E ^b  

^a UNIVERSITY OF NORTHERN IOWA   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Bessel functions; Correlation functions; Importance sampling; Mixtures; Model determination; Stationary process

Indexed keywords

EID: 0041392649     PISSN: 10857117     EISSN: None     Source Type: Journal    
DOI: 10.2307/1400508     Document Type: Article

References (36)

1. Akaike, H. (1973), "Information Theory and an Extension of Maximum Likelihood Principle," in Second International Symposium on Information Theory, eds. B. Petrov and F. Csáki, Budapest: Akadémia Kiadó, pp. 267-281.
2. Armstrong, M., and Diamond, P. (1984), "Testing Variograms for Positive Definiteness," Math Geology, 24, 135-147.
3. Armstrong, M., and Jabin, R. (1981), "Variogram Models Must Be Positive Definite," Math Geology, 13, pp. 455-459.
4. Barry, R. P., and Ver Hoef, J. M. (1996), Blackbox Kriging: Spatial Prediction Without Specifying Variogram Models," Journal of Agricultural, Biological, and Environmental Statistics, 1, 297-322.
5. Cherry, S., Banfield, J., and Quimby, W. (1996), "An Evaluation of a Nonparametric Method of Estimating Semivariograms of Isotropic Spatial Process," Journal of Applied Statistics, 23, 435-449.
6. Chung, K. (1974), A Course in Probability Theory, New York: Academic Press.
7. Christakos, G. (1984), "On the Problem of Permissible Covariance and Variogram Models," Water Resources Research, 20, 251-265.
8. Cressie, N. (1985), "Fitting Variogram Models by Weighted Least Squares," Math Geology, 17, 563-586.
9. _ (1993), Statistics for Spatial Data, New York: Wiley.
10. DeOliveira, V., Kedem, B., and Short, D. (1997), "Bayesian Prediction of Transformed Gaussian Random Fields," technical report, Department of Mathematics, University of Maryland, College Park, MD.
11. Diggle, P., Liang, K-L., and Zeger, S. (1994), Analysis of Longitudinal Data, New York: Oxford Science Publications.
12. Ecker, M., and Heltshe, J. (1994), "Geostatistical Estimates of Scallop Abundance," in Case Studies in Biometry, eds. N. Lange, L. Ryan, L. Billard, D. Brillinger, L. Conquest, and J. Greenhouse, New York: Wiley, pp. 107-124.
13. Feller, W. (1966), An Introduction to Probability Theory and its Applications, Volume II, New York: Wiley.
14. Gaudard, M., Karson, M., Linder, E., and Sinha, D. (1995), "Modeling Precipitation Using Bayesian Spatial Analysis," in Proceedings of the Section on Bayesian Inference, American Statistical Association, pp. 173-177.
15. Gelfand, A. E., and Ghosh, S. K. (in press), "Model Choice: A Minimum Posterior Predictive Loss Approach," Biometrika, 85.
16. Hall, P., Fisher, N., and Hoffmann, B. (1994), "On the Nonparametric Estimation of Covariance Functions," The Annals of Statistics, 22, 2115-2134.
17. Handcock, M., and Stein, M. (1993), "A Bayesian Analysis of Kriging," Technometrics. 35, 403-410.
18. Handcock, M., and Wallis, J. (1994), "An Approach to Statistical Spatial-Temporal Modeling of Meteorological Fields (with discussion)," Journal of the American Statistical Association, 89, 368-390.
19. Journel, A., and Huijbregts, C. (1978), Mining Geostatistics, New York: Academic Press.
20. Journel, A., and Rossi, M. (1989), "When Do We Need a Trend Model in Kriging?" Math Geology. 21, 715-739.
21. Kadane, J., and Dickey, J. (1980), "Bayesian Decision Theory and the Simplification of Models," in Evaluations of Econometric Models, eds. J. Kmenta and J. Ramsey, New York: Academic Press, pp. 245-268.
22. Kaluzny, S., Vega, S., Cardosa, T., and Shelly, A. (1996), S+SpatialStats User's Manual, Seattle: MathSoft Inc.
23. Lele, S. (1995), "Inner Product Matrices, Kriging, and Nonparametric Estimation of Variogram," Math Geology, 27, 673-692.
24. Mantoglou, A., and Wilson, J. (1982), "The Turning Bands Methods for Simulation of Random Fields Using Line Generation by Spectral Method," Water Resources Research, 18, 1379-1394.
25. Matheron, G. (1963), "Principles of Geostatistics," Economic Geology, 58, 1246-1266.
26. McBratney, A., and Webster, R. (1986), "Choosing Functions for Semi-Variograms of Soil Properties and Fitting Them to Sampling Estimates," Journal of Soil Science, 37, 617-639.
27. McCullagh, P., and Neider, J. (1989), Generalized Linear Models, New York: Chapman and Hall.
28. Sampson, P., and Guttorp, P. (1992), "Nonparametric Estimation of Nonstationary Spatial Covariance Structure. Journal of the American Statistical Association, 87, 108-119.
29. Schoenberg, I. (1938), "Metric Spaces and Completely Monotone Functions," Annals of Mathematics, 39, 811-841.
30. Schwartz, G. (1978), "Estimating the Dimension of a Model," Annals of Statistics, 6, 461-464.
31. Shapiro, A., and Botha, J. (1991), "Variogram Fitting With a General Class of Conditionally Nonnegative Definite Functions," Computational Statistics and Data Analysis, 11, 87-96.
32. Smith, A. F. M., and Gelfand, A. E. (1992), "Bayesian Statistics Without Tears: A Sampling-Resampling Perspective," The American Statistician, 46, 84-88.
33. Webster, R., and McBratney, A. (1989), "On the Akaike Information Criterion for Choosing Models for Variograms of Soil Properties," Journal of Soil Science, 40, 493-496.
34. West, M. (1993), "Approximating Posterior Distributions by Mixtures," Journal of the Royal Statistical Society, Ser. B, 55, 563-586.
35. Yaglom, A. (1987), Correlation Theory of Stationary and Related Random Functions I, New York: Springer-Verlag.
36. Zellner, A. (1994), "Bayesian and Non-Bayesian Estimation Using Balanced Loss Functions," in Statistical Decision Theory and Related Topics, V, eds. S. Gupta and J. Berger, New York: Springer-Verlag, pp. 377-390.