Abstract
The problem of spatial sampling design for estimating a multivariate random field from information obtained by sampling related variables is considered. A formulation assigning different degrees of importance to the variables and locations involved is introduced. Adopting an entropy-based approach, an objective function is defined as a linear combination in terms of the amount of information on the variables and/or the locations of interest contained in the data. In the multivariate Gaussian case, the objective function is obtained as a geometric mean of conditional covariance matrices. The effect of varying the degrees of importance for the variables and/or the locations of interest is illustrated in some numerical examples.
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Bueso, M.C., Angulo, J.M., Cruz-Sanjulián, J. et al. Optimal Spatial Sampling Design in a Multivariate Framework. Mathematical Geology 31, 507–525 (1999). https://doi.org/10.1023/A:1007511923053
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DOI: https://doi.org/10.1023/A:1007511923053