Modeling Complex Spatial Dependencies: Low-Rank Spatially Varying Cross-Covariances With Application to Soil Nutrient Data

Journal of Agricultural, Biological, and Environmental Statistics

Volumn 18, Issue 3, 2013, Pages 274-298

  Guhaniyogi, Rajarshi ^a   Finley, Andrew O ^b   Banerjee, Sudipto ^c   Kobe, Richard K ^b  

^a Duke University   (United States)

^b MICHIGAN STATE UNIVERSITY   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Gaussian spatial process; MCMC; Nonstationarity; Predictive process; Tropical soil nutrients

Indexed keywords

COVARIANCE ANALYSIS; DATA SET; GAUSSIAN METHOD; GEOSTATISTICS; NUMERICAL MODEL; SOIL NUTRIENT; SPATIAL DATA; SPATIAL VARIATION; TROPICAL SOIL;

COSTA RICA; LA SELVA BIOLOGICAL STATION; LIMON;

EID: 84884672062     PISSN: 10857117     EISSN: 15372693     Source Type: Journal    
DOI: 10.1007/s13253-013-0140-3     Document Type: Article

References (48)

1. Apanasovich, T. V., and Genton, M. G. (2010), "Cross-Covariance Functions for Multivariate Random Fields Based on Latent Dimensions," Biometrika, 97, 15-30.
2. Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2004), Hierarchical Modeling and Analysis for Spatial Data, Boca Raton: Chapman and Hall/CRC Press.
3. Banerjee, S., and Johnson, G. A. (2006), "Coregionalized Single- and Multi-Resolution Spatially-Varying Growth Curve Modelling With Application to Weed Growth," Biometrics, 61, 617-625.
4. Banerjee, S., Gelfand, A. E., Finley, A. O., and Sang, H. (2008), "Gaussian Predictive Process Models for Large Spatial Datasets," Journal of the Royal Statistical Society, Series B, 70, 825-848.
5. Banerjee, S., Finley, A. O., Waldmann, P., and Ericcson, T. (2010), "Hierarchical Spatial Process Models for Multiple Traits in Large Genetic Trials," Journal of the American Statistical Association, 105, 506-521.
6. Cressie, N. (1993), Statistics for Spatial Data (2nd ed.), New York: Wiley.
7. Cressie, N., and Johannesson, G. (2008), "Fixed Rank Kriging for Very Large Spatial Data Sets," Journal of the Royal Statistical Society, Series B, 70, 209-226.
8. Cressie, N. A. C., and Wikle, C. K. (2011), Statistics for Spatio-Temporal Data, New York: Wiley.
9. Daniels, M. J., and Kass, R. E. (1999), "Nonconjugate Bayesian Estimation of Covariance Matrices and Its Use in Hierarchical Models," Journal of the American Statistical Association, 94, 1254-1263.
10. Diez, J. M., and Pulliam, H. R. (2007), "Hierarchical Analysis of Species Distributions and Abundance Across Environmental Gradients," Ecology, 88, 3144-3152.
11. Finley, A. O., Banerjee, S., and McRoberts, R. E. (2009), "Hierarchical Spatial Models for Predicting Tree Species Assemblages Across Large Domains," Annals of Applied Statistics, 3, 1052-1079.
12. Finley, A. O., Banerjee, S., Ek, A. R., and McRoberts, R. E. (2008), "Bayesian Multivariate Process Modeling for Prediction of Forest Attributes," Journal of Agricultural, Biological, and Environmental Statistics, 13, 60-83.
13. Finley, A. O., Sang, H., Banerjee, S., and Gelfand, A. E. (2009), "Improving the Performance of Predictive Process Modeling for Large Datasets," Computational Statistics & Data Analysis, 53, 2873-2884.
14. Finzi, A. C., van Breemen, N., and Canham, C. D. (1998), "Canopy Tree-Soil Interactions Within Temperate Forests: Species Effects on pH and Base Cations," Ecological Applications, 8, 447-454.
15. Gelfand, A. E., and Banerjee, S. (2010), "Multivariate Spatial Process Models," in Handbook of Spatial Statistics, eds. A. E. Gelfand, P. Diggle, P. Guttorp, and M. Fuentes, Boca Raton: Taylor and Francis/CRC, pp. 495-516.
16. Gelfand, A. E., and Ghosh, S. K. (1998), "Model Choice: A Minimum Posterior Predictive Loss Approach," Biometrika, 85, 1-11.
17. Gelfand, A. E., Schmidt, A. M., Banerjee, S., and Sirmans, C. F. (2004), "Nonstationary Multivariate Process Modeling Through Spatially Varying Coregionalization" (with discussion), Test, 13, 263-312.
18. Gelman, A., and Rubin, D. (1992), "Inference From Iterative Simulation Using Multiple Sequences," Statistical Science, 7, 457-511.
19. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004), Bayesian Data Analysis (2nd ed.), Boca Raton: Chapman and Hall/CRC Press.
20. Gneiting, T., and Guttorp, P. (2010), "Continuous-Parameter Stochastic Process Theory," in Handbook of Spatial Statistics, eds. A. E. Gelfand, P. Diggle, P. Guttorp, and M. Fuentes, Boca Raton: Taylor and Francis/CRC, pp. 17-28.
21. Gneiting, T., Kleiber, W., and Schlather, M. (2010), "Matérn Cross-Covariance Functions for Multivariate Random Fields," Journal of the American Statistical Association, 105, 1167-1177.
22. Guhaniyogi, R., Finley, A. O., Banerjee, S., and Gelfand, A. E. (2011), "Adaptive Gaussian Predictive Process Models for Large Spatial Datasets," Environmetrics, 22, 997-1007.
23. Harville, D. A. (1997), Matrix Algebra From a Statistician's Perspective, New York: Springer.
24. Henderson, H. V., and Searle, S. R. (1981), "On Deriving the Inverse of a Sum of Matrices," SIAM Review, 23, 53-60.
25. Hodges, J. S., and Reich, B. J. (2010), "Adding Spatially-Correlated Errors Can Mess up the Fixed Effect You Love," American Statistician, 64, 335-344.
26. Holste, E. K., Kobe, R. K., and Vriesendorp, C. F. (2011), "Seedling Growth Responses to Soil Nutrients in a Wet Tropical Forest Understory," Ecology, 92, 1828-1838.
27. Houlton, B. Z., Wang, Y. P., Vitousek, P. M., and Field, C. B. (2008), "A Unifying Framework for Dinitrogen Fixation in the Terrestrial Biosphere," Nature, 454, 327-331.
28. Kang, E. L., and Cressie, N. (2011), "Bayesian Inference for the Spatial Random Effects Model," Journal of the American Statistical Association, 106, 972-983.
29. Kobe, R. K., and Vriesendorp, C. F. (2009), "Size of Sampling Unit Strongly Influences Detection of Seedling Limitation in a Wet Tropical Forest," Ecology Letters, 12, 220-228.
30. Majumdar, A., Paul, D., and Bautista, D. (2010), "A Generalized Convolution Model for Multivariate Nonstationary Spatial Processes," Statistica Sinica, 20, 675-695.
31. McCarthy-Neumann, S., and Kobe, R. K. (2010), "Conspecific Plant-Soil Feedbacks Reduce Survivorship and Growth of Tropical Tree Seedlings," Journal of Ecology, 98, 396-407.
32. Ovaskainen, O., Hottola, J., and Siitonen, J. (2010), "Modeling Species Co-occurrence by Multivariate Logistic Regression Generates New Hypotheses on Fungal Interactions," Ecology, 9, 2414-2521.
33. Paciorek, C. J. (2010), "The Importance of Scale for Spatial-Confounding Bias and Precision of Spatial Regression Estimators," Statistical Science, 107-125.
34. Pourahmadi, M. (1999), "Joint Mean-Covariance Model With Applications to Longitudinal Data: Unconstrained Parameterisation," Biometrika, 86, 677-690.
35. Rao, C. R. (1973), Linear Statistical Inference and Its Applications (2nd ed.), New York: Wiley.
36. Robert, C. P., and Casella, G. (2010), An Introduction to Monte Carlo Methods With R, New York: Springer.
37. Roberts, G. O., and Rosenthal, J. S. (2009), "Examples of Adaptive MCMC," Journal of Computational and Graphical Statistics, 18, 349-367.
38. Royle, J. A., and Berliner, L. M. (1999), "A Hierarchical Approach to Multivariate Spatial Modeling and Prediction," Journal of Agricultural, Biological, and Environmental Statistics, 4, 29-56.
39. Sang, H., Jun, M., and Huang, J. Z. (2011), "Covariance Approximation for Large Multivariate Spatial Data Sets With an Application to Multiple Climate Model Errors," Annals of Applied Statistics, 4, 2519-2548.
40. Stein, M. L. (1999), Interpolation of Spatial Data: Some Theory of Kriging, New York: Springer.
41. - (2008), "A Modeling Approach for Large Spatial Datasets," Journal of the Korean Statistical Society, 37, 3-10.
42. Townsend, A. R., Asner, G. P., and Cleveland, C. C. (2008), "The Biogeochemical Heterogeneity of Tropical Soils," Trends in Ecology & Evolution, 23, 424-431.
43. Wackernagel, H. (2006), Multivariate Geostatistics: An Introduction With Applications (3rd ed.), New York: Springer.
44. Waddle, J. H., Dorazio, R. M., Walls, S. C., Rice, K. G., Beauchamp, J., Schuman, M. J., and Mazzotti, F. J. (2010), "A New Parameterization for Estimating Co-occurrence of Interacting Species," Ecological Applications, 20, 1467-1475.
45. Walker, T. W., and Syers, J. K. (1976), "The Fate of Phosphorus During Pedogenesis," Geoderma, 15, 1-19.
46. Wardle, D. A., Walker, L. R., and Bardgett, R. D. (2004), "Ecosystem Properties and Forest Decline in Contrasting Long-Term Chronosequences," Science, 305, 509-512.
47. Yaglom, A. M. (1987), Correlation Theory of Stationary and Related Random Functions, Vol. I, New York: Springer.
48. Zhang, H. (2007), "Maximum-Likelihood Estimation for Multivariate Spatial Linear Coregionalization Models," Environmetrics, 18, 125-139.