Data Fusion in a Spatial Multivariate Framework: Trading off Hypotheses Against Information
Due to the exponential growth in the amount and diversity of data that one may expect to provide greater modeling and predictions opportunities, there is a real need for methods that aim at reconciling them inside a flexible and sound theoretical framework. In a geostatistical prediction context, beside more or less straighforward variations around univariate kriging (e.g. kriging with external drift), the most classical method (i.e. cokriging) is based on a multivariate random field approach of the problem, at the price of strong modeling hypotheses. However, there are expected practical situations where these hypotheses may be hard to fulfill or do not make sense from a modeling viewpoint.
This paper proposes an alternative way of using secondary information for spatial prediction. Based on a data fusion perspective, a general theoretical procedure is proposed. Simple cokriging and Bayesian data fusion are compared both from theoretical and practical viewpoints. Theoretical differences are first emphasized based on the corresponding modeling hypotheses. A case study based on synthetic data subsequently allows to compare both methods from a practical viewpoint. It is shown that, in spite of some simplifying hypotheses required by data fusion, the method is offering quite comparable performances in situations where simple cokriging is expected to be the best possible predictor. Moreover, it offers a much greater flexibility and opens new avenues for incorporating a wide panel of very different and possibly numerous secondary information that, by nature, would not easily fit into a multivariate random field framework, as required by cokriging.
KeywordsRoot Mean Square Error Covariance Function Data Fusion Practical Viewpoint Relative Root Mean Square Error
Unable to display preview. Download preview PDF.
- Bogaert P, Fasbender D (2007) Bayesian data fusion in a spatial prediction context: A general formulation. Stochastic Environmental Research and Risk Assessment. Published onlineGoogle Scholar
- Chilès J.-P, Delfiner P (1999) Geostatistics: modeling spatial uncertainty. John Wiley and Sons, Inc., New York, NYGoogle Scholar
- Christakos G (1992) Random field models in earth sciences. Academic Press, San Diego, CAGoogle Scholar
- Cressie N (1991) Statistics for spatial data. Wiley series in probability and mathematical statistics. John Wiley and Sons, Inc., New York, NYGoogle Scholar
- Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York, NYGoogle Scholar