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Interpolation with uncertain spatial covariances: A Bayesian alternative to Kriging

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  • Le, Nhu D.
  • Zidek, James V.

Abstract

In this paper a Bayesian alternative to Kriging is developed. The latter is an important tool in geostatistics. But aspects of environmetrics make it less suitable as a tool for interpolating spatial random fields which are observed successively over time. The theory presented here permits temporal (and spatial) modeling to be done in a convenient and flexible way. At the same time model misspecifications, if any, can be corrected by additional data if and when it becomes available, and past data may be used in a systematic way to fit model parameters. Finally, uncertainty about model parameters is represented in the (posterior) distributions, so unrealistically small credible regions for the interpolants are avoided. The theory is based on the multivariate normal and related distributions, but because of the hierarchical prior models adopted, the results would seem somewhat robust with respect to the choice of these distributions and associated hyperparameters.

Suggested Citation

  • Le, Nhu D. & Zidek, James V., 1992. "Interpolation with uncertain spatial covariances: A Bayesian alternative to Kriging," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 351-374, November.
    • Handle: RePEc:eee:jmvana:v:43:y:1992:i:2:p:351-374
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    Citations

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    Cited by:

    1. Idris A. Eckley & Guy P. Nason & Robert L. Treloar, 2010. "Locally stationary wavelet fields with application to the modelling and analysis of image texture," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(4), pages 595-616, August.
    2. Christopher K. Wikle, 2003. "Hierarchical Models in Environmental Science," International Statistical Review, International Statistical Institute, vol. 71(2), pages 181-199, August.
    3. Sun, Xiaoqian & He, Zhuoqiong & Kabrick, John, 2008. "Bayesian spatial prediction of the site index in the study of the Missouri Ozark Forest Ecosystem Project," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3749-3764, March.
    4. Sujit K. Sahu & Alan E. Gelfand & David M. Holland, 2010. "Fusing point and areal level space–time data with application to wet deposition," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(1), pages 77-103, January.
    5. Peter Diggle & Soren Lophaven, 2004. "Bayesian Geostatistical Design," Johns Hopkins University Dept. of Biostatistics Working Paper Series 1042, Berkeley Electronic Press.
    6. Stefano F. Tonellato, 2005. "Identifiability Conditions for Spatio-Temporal Bayesian Dynamic Linear Models," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 81-101.
    7. Soumen Dey & Mohan Delampady & Ravishankar Parameshwaran & N. Samba Kumar & Arjun Srivathsa & K. Ullas Karanth, 2017. "Bayesian Methods for Estimating Animal Abundance at Large Spatial Scales Using Data from Multiple Sources," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(2), pages 111-139, June.
    8. Hongxing Li & Charlotte D. Smith & Li Wang & Zheng Li & Chuanlong Xiong & Rong Zhang, 2019. "Combining Spatial Analysis and a Drinking Water Quality Index to Evaluate Monitoring Data," IJERPH, MDPI, vol. 16(3), pages 1-9, January.

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