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Spatial Prediction Based on the Bayesian Kriging with Box-Cox Transformation

  • Published : 2009.09.30

Abstract

In the last decades, there has been much interest in climate variability because its change has dramatic effects on humanity. Especially, the precipitation data are measured over space and their spatial association is so complicated. So we should take into account such a spatial dependency structure while analyzing the data. However, in linear models for analyzing the data, data sets show severely skewed distribution. In the paper, we consider the Box-Cox transformation to satisfy the normal distribution prior to the analysis, and employ a Bayesian hierarchical framework to investigate the spatial patterns. The data set we considered is monthly average precipitation of the third quarter of 2007 obtained from 347 automated monitoring stations in Contiguous South Korea.

Keywords

References

  1. Banerjee, S., Carlin, B. P. and Gelfand, A. E. (2004). Hierarchical Modeling and Analysis for Spatial Data, Chapman & Hall/CRC, Florida
  2. Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations, Journal of the Royal Statistical Society, Series B, 26, 211-246
  3. Brown, P. J., Le, N. D. and Zidek, J. V. (1994). Multivariate spatial interpolation and exposure to air pollutants, Canadian Journal of Statistics, 22, 489-509 https://doi.org/10.2307/3315406
  4. Cressie, N., Frey, J., Harch, B. and Smith, M. (2006). Spatial prediction on a river network, Journal of Agricultural, Biological, and Environmental Statistics, 11, 127-150 https://doi.org/10.1198/108571106X110649
  5. 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 https://doi.org/10.2307/2965412
  6. Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998). Model-based geostatistics (with discussion), Applied Statistics, 47, 299-350 https://doi.org/10.1111/1467-9876.00113
  7. Ecker, M. D. and Gelfand, A. E. (1997). Bayesian variogram modeling for an isotropic spatial process, Journal of Agricultural, Biological, and Environmental Statistics, 2, 347-369 https://doi.org/10.2307/1400508
  8. Finley, A. O., Banerjee, S. and Carlin, B. P. (2008). spBayes: Univariate and Multivariate Spatial Modeling, R package version 0.1-0
  9. Handcock, M. S. and Stein, M. L. (1993). A Bayesian analysis of kriging, Technometrics, 35, 403-410 https://doi.org/10.2307/1270273
  10. Handcock, M. S. and Wallis, J. R. (1994). An approach to statistical spatio-temporal modeling of meteorological fields, Journal of the American Statistical Association, 89, 368-378 https://doi.org/10.2307/2290832
  11. Heo, T. Y. and Park, M. S. (2009). Bayesian spatial modeling of precipitation data, Korean Journal of Applied Statistics, 22, 425-433 https://doi.org/10.5351/KJAS.2009.22.2.425
  12. Karson, M. J., Gaudard, M., Linder, E. and Sinha, D. (1999). Bayesian analysis and computations for spatial prediction (with discussion), Environmental and Ecological Statistics, 6, 147-182 https://doi.org/10.1023/A:1009614003692
  13. Le, N. D. and Zidek, J. V. (1992). Interpolation with uncertain spatial covariance: A Bayesian alter-native to Kriging, Journal of Multivariate Analysis, 43, 351-374 https://doi.org/10.1016/0047-259X(92)90040-M
  14. Park, M. S. and Heo, T. Y. (2009). Seasonal spatial-temporal model for rainfall data of South Korea, Journal of Applied Sciences Research, 5, 565-572
  15. R Development Core Team (2008). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing. Vienna, Austria, ISBN 3-900051-07-0
  16. Ribeiro, P. J. and Diggle, P. J. (2001). geoR: A package for geostatistical analysis, R-NEWS, 1, 15-18
  17. Roberts, G. O. (1996). Markov Chain Concepts Related to Sampling Algorithms, in Markov Chain Monte Carlo in Practice, edited by W. R. Gilks, S. Richardson and D. J. Spiegeihalter. Chapman & Hall/CRC, London, 45-57
  18. Schabenberger, O. and Gotway, C. A. (2004). Statistical Methods for Spatial Data Analysis, Chapman & Hall/CRC, Florida
  19. Smith, R. L., Kolenikov, S. and Cox, L. H. (2003). Spatiotemporal modeling of PM2.5 data with missing values, Journal of Geophysical Research, 108, STS 11-1

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  1. On the Hierarchical Modeling of Spatial Measurements from Different Station Networks vol.26, pp.1, 2013, https://doi.org/10.5351/KJAS.2013.26.1.093