Graduate Thesis Or Dissertation
 

The design-based Empirical Orthogonal Functions model : an alternative for the analysis of spatio-temporal data

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  • Random processes are monitored over space and time by a network of stations distributed across a spatial region. Researchers have developed several analysis techniques to model the random process. Some of them require assumptions on the spatio-temporal variability of the process. An alternative method to analyze spatio-temporal data that does not require any assumption on the variance-covariance matrix is the Empirical Orthogonal Functions (EOF) model. The spatial distribution of the network sites influences the accuracy of the prediction results obtained by the EOF model. Researchers have proposed different methods to address this problem. We propose a model, the design-based EOF model, that incorporates information on the spatio-temporal variability of the process captured by the sampling design used to establish the network. The theoretical development of the model and an application are presented. We also consider the inclusion of auxiliary information into the design-based EOF model with the purpose of interpolating the process to unvisited sites. Interpolation results from the design-based EOF model are illustrated by considering a real data set and compared to spatial interpolation results obtained by using ordinary kriging. With the desire of making the design-based EOF model accessible to those monitoring programs that did not use a sampling probability design to establish the monitoring network, we consider two approaches that provide proper weights to be used in the model.
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