Abstract
An objective for applying a Crop Simulation Model (CSM) in precision agriculture is to explain the spatial variability of crop performance and to help guide decisions related to the site-specific management of crop inputs. CSMs require inputs related to soil, climate, management, and crop genetic information to simulate crop yield. In practice, however, measuring these inputs at the desired high spatial resolution is prohibitively expensive. We propose a Bayesian modeling framework that melds a CSM with sparse data from a yield monitoring system to deliver location specific posterior predicted distributions of yield and associated unobserved spatially varying CSM parameter inputs. These products facilitate exploration of process-based explanations for yield variability. The proposed Bayesian melding model consists of a systemic component representing output from the physical model and a residual spatial process that compensates for the bias in the physical model. The spatially varying inputs to the systemic component arise from a multivariate Gaussian process, while the residual component is modeled using a univariate Gaussian process. Due to the large number of observed locations in the motivating dataset, we seek dimension reduction using low-rank predictive processes to ease the computational burden. The proposed model is illustrated using the Crop Environment Resources Synthesis (CERES)-Wheat CSM and wheat yield data collected in Foggia, Italy.
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Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2004), Hierarchical Modeling and Analysis for Spatial Data, Boca Raton: Chapman and Hall/CRC Press.
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.
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.
Basso, B., Bertocco, M., Sartori, L., and Martin, E. C. (2007), “Analyzing the Effects of Climate Variability on Spatial Pattern of Yield in a Maize-Wheat-Soybean Rotation,” European Journal of Agronomy, 26, 81–91.
Basso, B., Cammarano, D., Troccoli, A., Chen, D., and Ritchie, J. T. (2010), “Long-Term Wheat Response to Nitrogen in a Rainfed Mediterranean Environment: Field Data and Simulation Analysis,” European Journal of Agronomy, 33, 132–138.
Basso, B., Ritchie, J. T., Cammarano, D., and Sartori, L. (2011), “A Strategic and Tactical Management Approach to Select Optimal N Fertilizer Rates for Wheat in a Spatially Variable Field,” European Journal of Agronomy, doi:10.1016/j.eja.2011.06.004.
Batchelor, W. D., Basso, B., and Paz, J. O. (2002), “Examples of Strategies to Analyze Spatial and Temporal Yield Variability Using Crop Models,” European Journal of Agronomy, 18, 141–158.
Cambardella, C. A., Colvin, T. S., Karlen, D. S., Logsdon, S. D., Berry, E. C., Radke, J. K., Kaspar, T. C., Parkin, T. B., and Jaynes, D. B. (1996), “Soil Properties Contribution to Yield Variation Pattern,” in Proc. 3rd Intl. Conf. on Precision Agriculture, eds. Robert et al., Madison: ASA-CSSA-SSSA, pp. 217–224.
Carlin, B. P., and Louis, T. A. (2000), Bayes and Empirical Bayes Methods for Data Analysis (2nd ed.), Boca Raton: Chapman and Hall/CRC Press.
Cressie, N. A. C. (1993), Statistics for Spatial Data (2nd ed.), New York: Wiley.
Cressie, N. A. C., and Johannesson, G. (2008), “Spatial Prediction for Massive Datasets,” Journal of the Royal Statistical Society Series B, 70, 209–226.
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.
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.
Flegal, J. M., Haran, M., and Jones, G. L. (2008), “Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?” Statistical Science, 23, 250–260.
Fuentes, M., and Raftery, A. E. (2005), “Model Evaluation and Spatial Interpolation by Bayesian Combination of Observations With Outputs From Numerical Models,” Biometrics, 66, 36–45.
Gelfand, A. E., and Ghosh, S. K. (1998), “Model Choice: A Minimum Posterior Predictive Loss Approach,” Biometrika, 85, 1–11.
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.
Gelman, A., and Rubin, D. (1992), “Inference From Iterative Simulation Using Multiple Sequences”, Statistical Science, 7(4), 457–511.
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.
Harville, D. A. (1997), Matrix Algebra from a Statistician’s Perspective, New York: Springer.
He, J., Jones, J. W., Graham, W. D., and Dukes, M. D. (2010), “Influence of Likelihood Function Choice for Estimating Crop Model Parameters Using the Generalized Likelihood Uncertainty Estimation Method,” Agricultural Systems, 103, 256–264.
Henderson, H. V., and Searle, S. R. (1981), “On Deriving the Inverse of a Sum of Matrices,” SIAM Review, 23, 53–60.
Higdon, D. M. (2002), “Space and Space-Time Modeling Using Process Convolutions,” in Quantitative Methods for Current Environmental Issues, eds. C. Anderson, V. Barnett, P. C. Chatwin, and A. H. El-Shaarawi, Berlin: Springer, pp. 37–56.
Jones, J., Hoogenboom, G., Porter, C., Boote, K., Batchelor, W., Hunt, L., Wilkens, P., Singh, U., Gijsman, A., and Ritchie, J. (2003), “The DSSAT Model Cropping System Model,” European Journal of Agronomy, 18, 235–265.
Jones, G. L., Haran, M., Caffo, B. S., and Neath, R. (2006), “Fixed-Width Output Analysis for Markov Chain Monte Carlo,” Journal of the American Statistical Association, 101, 1537–1547.
Kamman, E. E., and Wand, M. P. (2003), “Geoadditive Models,” Journal of the Royal Statistical Society. Series C, Applied Statistics, 52, 1–18.
Lin, X., Wahba, G., Xiang, D., Gao, F., Klein, R., and Klein, B. (2000), “Smoothing Spline ANOVA Models for Large Data Sets With Bernoulli Observations and the Randomized GACV,” Annals of Statistics, 28, 1570–1600.
Paciorek, C. J., and Schervish, M. J. (2006), “Spatial Modelling Using a New Class of Nonstationary Covariance Functions,” Environmetrics, 17, 483–506.
Pierce, F. J., and Nowak, P. (1999), “Aspects of Precision Agriculture,” Advances in Agronomy, 67, 1–85.
Poole, D. J., and Raftery, A. E. (2000), “Inference for Deterministic Simulation Models: The Bayesian Melding Approach,” Journal of the American Statistical Association, 95, 1244–1255.
Raftery, A. E., Givens, G. H., and Zeh, J. E. (1995), “Inference From a Deterministic Population Dynamics Model for Bowhead Whales” (with discussion), Journal of the American Statistical Association, 90, 402–430.
Rasmussen, C. E., and Williams, C. K. I. (2006), Gaussian Processes for Machine Learning, Cambridge: MIT Press.
Ratliff, L. F., Ritchie, J. T., and Cassel, D. K. (1983), “Field-Measured Limits of Soil Water Availability as Related to Laboratory-Measured Properties,” Soil Science Society of America Journal, 47, 770–775.
Ritchie, J. T. (1972), “A Model for Predicting Evaporation from a Row Crop with Incomplete Cover,” Water Resources Research, 8, 1204–1214.
Ritchie, J. T., and Otter, S. (1985), “Description and Performance of CERES-Wheat: A User-Oriented Wheat Yield Model,” in Agricultural Research Service, Wheat Yield Project, eds. J. T. Richie and S. Otter, Springfield: ARS 38 National Technical Information Service, pp. 159–175.
Robert, C. P. (2001), The Bayesian Choice (2nd ed.), New York: Springer.
Robert, C., and Casella, G. (2004), Monte Carlo Statistical Methods (2nd ed.), New York: Springer.
Stein, M. L. (2007), “Spatial Variation of Total Column Ozone on a Global Scale,” Annals of Applied Statistics, 1, 191–210.
— (2008), “A Modeling Approach for Large Spatial Datasets,” Journal of the Korean Statistical Society, 37, 3–10.
Sudduth, K. A., Drummond, S. T., Birrell, S. J., and Kitchen, N. R. (1996), “Analysis of Spatial Factors Influencing Crop Yield,” in Proc. 3rd Intl. Conf. on Precision Agriculture, eds. Robert et al., Madison: ASA-CSSA-SSSA, pp. 129–140.
Sun, Y., Li, B., and Genton, M. G. (2011), “Geostatistics for Large Datasets,” in Space-Time Processes and Challenges Related to Environmental Problems: Proceedings of the Spring School “Advances and Challenges in Space-time Modelling of Natural Events”, eds. E. Porcu, J. M. Montero, and M. Schlather, Berlin: Springer.
Ver Hoef, J. M., Cressie, N. A. C., and Barry, R. P. (2004), “Flexible Spatial Models Based on the Fast Fourier Transform (FFT) for Cokriging,” Computational Statistics & Data Analysis, 13, 265–282.
Wackernagel, H. (2003), Multivariate Geostatistics: An Introduction With Applications, Berlin: Springer.
Wikle, C. K., and Cressie, N. (1999), “A Dimension Reduced Approach to Space-Time Kalman Filtering,” Biometrika, 86, 815–829.
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Finley, A.O., Banerjee, S. & Basso, B. Improving Crop Model Inference Through Bayesian Melding With Spatially Varying Parameters. JABES 16, 453–474 (2011). https://doi.org/10.1007/s13253-011-0070-x
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DOI: https://doi.org/10.1007/s13253-011-0070-x