We study spatial sampling design for prediction of stationary isotropic Gaussian processes with estimated parameters of the covariance function. The key issue is how to incorporate the parameter uncertainty into design criteria to correctly represent the uncertainty in prediction. Several possible design criteria are discussed that incorporate the parameter uncertainty. A simulated annealing algorithm is employed to search for the optimal design of small sample size and a two-step algorithm is proposed for moderately large sample sizes. Simulation results are presented for the Matérn class of covariance functions. An example of redesigning the air monitoring network in EPA Region 5 for monitoring sulfur dioxide is given to illustrate the possible differences our proposed design criterion can make in practice.

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Singular Value Decomposition (SVD) is a useful tool in Functional Data Analysis (FDA).Compared to Principal Component Analysis (PCA), SVD is more fundamental, because SVD simultaneously provides the PCAs in both row and column spaces. We compare SVD and PCA from the FDA view point, and extend the usual SVD to variations by considering different centerings. A generalized scree plot is proposed to select an appropriate centering in practice.Several matrix views of the SVD components are introduced to explore different features in data, including SVD surface plots, rotation movies, curve movies and image plots. These methods visualize both column and row information of a two-way matrix simultaneously, relate the matrix to relevant curves, show local variations and interactions between columns and rows. Severaltoy examples are designed to compare as well as reveal the different variations of SVD, and real data examples are used to illustrate the usefulness of the visualization methods.