Abstract:
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There is a large literature on the design of sampling networks for univariate spatial data in two-dimensional Euclidean space, some of which has recently been extended to multivariate spatial data in Euclidean space or specialized to univariate data on stream networks. We take up the heretofore unconsidered problem of model-based sampling design for multivariate spatial prediction on a stream network. In particular, we study the extent to which optimal or near-optimal designs for multivariate prediction are collocated (i.e., all variables measured at every sampling site) when the multivariate covariance structure is separable, non-separable but of the same type (tail-up or tail-down dependence) across variables, or of different types across variables. Implications for crowd-sourced or volunteer water monitoring programs are noted.
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