Analyzing nonstationary spatial data using piecewise Gaussian processes

Journal of the American Statistical Association

Volumn 100, Issue 470, 2005, Pages 653-668

  Kim, Hyoung Moon ^a   Mallick, Bani K ^b   Holmes, C C ^c  

^a Konkuk University   (South Korea)

^b TEXAS A AND M UNIVERSITY   (United States)

^c UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Bayes factor; Kriging; Model averaging; Reversible jump Markov chain Monte Carlo; Voronoi tessellation

Indexed keywords

EID: 20444461640     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214504000002014     Document Type: Article

References (42)

1. Barman, I., Sharma, A. K., Walker, R. F., and Datta-Gupta, A. (1998), "Permeability Predictions in Carbonate Reservoirs Using Optimal Non-Parametric Transformations: An Application at the Salt Creek Field Unit, Kent County, TX," SPE 39667, presented at the 1998 SPE/DOE improved Oil Recovery Symposium, Tulsa, Oklahoma, April, 1998.
2. Berntsen, J., Espelid, T. O., and Genz, A. (1991a), "An Adaptive Algorithm for the Approximate Calculation of Multiple Integrals," ACM Transactions on Mathematical Software, 17, 437-451.
3. _ (1991b), "An Adaptive Multidimensional Integration Routine for a Vector of Integrals," ACM Transactions on Mathematical Software, 17, 452-456.
4. Brown, P. J., Le, N. D., and Zidek, J. V. (1994), "Multivariate Spatial Interpolation and Exposure To Air Pollutants," Canadian Journal of Statistics, 22, 489-505.
5. Canas, J. A. (1992), "Use of a Hydraulic Interwell Connectivity Concept for Sandstone Reservoir Characterization," unpublished masters thesis, Texas A&M University.
6. Cohen, A., and Jones, R. H. (1969), "Regression on a Random Field," Journal of the American Statistical Association, 64, 1172-1182.
7. Cressie, N. (1993), Statistics for Spatial Data (rev. ed.), New York: Wiley.
8. Creutin, J. D., and Obled, C. (1982), "Objective Analysis and Mapping Techniques for Rainfall Fields: An Objective Comparison," Water Resources Research, 18, 413-431.
9. De Oliveira, V., Kedem, B., and Short, D. S. (1997), "Bayesian Prediction of Transformed Gaussian Random Fields," Journal of the American Statistical Association, 92, 1422-1433.
10. Draper, D. (1995), "Assessment and Propagation of Model Uncertainty" (with discussion), Journal of the Royal Statistical Society, Ser. B, 57, 45-97.
11. Dromgoole, P., and Speers, R. (1997), "Geoscore: A Method for Quantifying Uncertainty in Field Reserve Estimates," Petroleum Geoscience, 3, 1-12.
12. Fuentes, M. (2001), "A New High-Frequency Kriging Approach for Nonstationary Environmental Processes," Environmetrics, 12, 469-483.
13. Fuentes, M., and Smith, R. (2001), "A New Class Of Nonstationary Spatial Models," technical report. North Carolina State University.
14. Gelfand, A. E. (1996), "Model Determination Using Sampling-Based Methods," in Markov Chain Monte Carlo in Practice, eds. W. R. Gilks, R. Richardson, and D. J. Spiegelhalter, Washington, DC: Chapman & Hall, pp.145-161.
15. Gelfand, A. E., Dey, D. K., and Chang, H. (1992), "Model Determination Using Predictive Distributions With Implementation via Sampling-Based Methods," Bayesian Statistics, 4, 147-167.
16. Green, P. J. (1995), "Reversible-Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination," Biometrika, 82, 711-732.
17. Green, P. J., and Sibson, R. (1978), "Computing Dirichlet Tessellations in the Plane," The Computer Journal, 21, 168-173.
18. Guttorp, P., and Sampson, P. (1994), "Methods for Estimating Heterogeneous Spatial Covariance Functions With Environmental Applications," in Handbook of Statistics 12, eds. G. P. Patil and C. R. Rao, New York: Elsevier Science, pp. 661-689.
19. Haas, T. C. (1990), "Kriging and Automated Variogram Modeling Within a Moving Window," Atmospheric Environment, 24A, 1759-1769.
20. _ (1995), "Local Prediction of a Spatio-Temporal Process With an Application to Wet Sulfate Deposition," Journal of the American Statistical Association, 90, 1189-1199.
21. Handcock, M. S., and Stein, M. L. (1993), "A Bayesian Analysis of Kriging," Technometrics, 35, 403-410.
22. 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.
23. Henderson, H. V., and Searle, S. R. (1981), "On Deriving the Inverse of a Sum of Matrices," SIAM Review, 23, 53-60.
24. Higdon, D. (2001), "Space and Space-Time Modeling Using Process Convolutions," technical report. Duke University.
25. Higdon, D., Swall, I., and Kern, J. (1999), "Nonstationary Spatial Modeling," in Bayesian Statistics 6, eds. J. M. Bernardo et al., Oxford, U.K.: Oxford University Press, pp. 761-768.
26. Kaluzny, S. P., Vega, S. C., Cardoso, T. P., and Shelly, A. A. (1997), S+SpatialStats, New York: Springer-Verlag.
27. Kass, R. E., and Raftery, A. E. (1995), "Bayes Factors," Journal of the American Statistical Association, 90, 773-795.
28. Le, N. D., and Zidek, J. V. (1992), "Interpolation With Uncertain Spatial Covariances: A Bayesian Alternative to Kriging," Journal of Multivariate Analysis, 43, 351-374.
29. Lee, S. H., and Datta-Gupta, A. (1999), "Electrofacies Characterization and Permeability Predictions in Carbonate Reservoirs: Role of Multivariate Analysis and Nonparametric Regression," SPE 56658, presented at the 1999 SPE Annual Technical Conference and Exhibition, Houston, Texas, October 1999.
30. Liang, E, and Wong, W. H. (2001), "Real-Parameter Evolutionary Sampling With Application in Bayesian Mixture Models," Journal of the American Statistical Association, 96, 653-666.
31. Nott, D. J., and Dunsmuir, T. M. (2002), "Estimation of Nonstationary Spatial Covariance Structure," Biometrika, 89, 819-829.
32. Nychka, D., Wikle, C., and Royle, J. A. (1999), "Large Spatial Prediction Problems and Nonstationary Random Fields," preprint. Geophysical Statistical Program, National Center for Atmospheric Research.
33. Okabe, A., Boots, B., and Sugihara, K. (1992), Spatial Tessellations, New York: Wiley.
34. Peddibhotla, S., Cubillos, H., Datta-Gupta, A., and Wu, C. H. (1996), "Rapid Simulation of Multiphase Flow Through Fine-Scale Geostatistical Realizations Using a New 3-D Streamline Model: A Field Example," SPE 36008, presented at PCC, Dallas, June 1996.
35. Sampson, P. D., Damian, D., and Guttorp, P. (2001), "Advances in Modeling and Inference for Environmental Processes With Nonstationary Spatial Covariance," in GeoENV 2000: Geostatistics for Environmental Applications, eds. E. Monesteiz, D. Allard, and R. Froidvaux, Dordrecht: Kluwer Academic, pp. 17-32.
36. Sampson, P. D., and Guttorp, P. (1992), "Nonparametric Estimation of Nonstationary Spatial Covariance Structure," Journal of the American Statistical Association, 87, 108-119.
37. Schmidt, A. M., and O'Hagan, A. (2003), "Bayesian Inference for Nonstationary Spatial Covariance Structure via Spatial Deformations," Journal of Royal Statistical Society, Ser. B, 65, 743-758.
38. Schon, J. H. (1996), Physical Properties of Rocks: Fundamentals and Principles of Petrophysics, New York: Pergamon Press.
39. Smith, R. L. (1996), "Estimating Nonstationary Spatial Correlation," preprint, University of North Carolina.
40. Stein, M. L. (1999), Statistical Interpolation of Spatial Data: Some Theory for Kriging, New York: Springer-Verlag.
41. Tanner, M. A. (1996), Tools for Statistical Inference, New York: Springer-Verlag.
42. Yaglom, A. M. (1987), Correlation Theory of Stationary and Related Random Functions I. Basic Results, New York: Springer-Verlag.