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Abstract:
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Characterizing the spatial dependency within the spatial temporal observations plays a critical role in modeling, interpretations, and predictions. As a widely used model, Markov random field (MRF) has shown both theoretical advantages and practical flexibilities on modeling both the linear and nonlinear dependency. Regardless its successes in practice, assessments of MRF is largely an open question. In this paper, focusing on the Gaussian MRF (GMRF), we propose an easily implemented procedure to assess the GMRF based on spatial temporal observations. The new procedure is flexible in practice and can be applied to assess a large number of structures including the isotropic and directional dependency as well as the Matern classes. Under very mild assumptions on the temporal dependency, theoretical guarantees for the proposed method are developed. A comprehensive simulation study has been conducted to demonstrate the finite sample performance of the procedure. Motivated from the efforts on modeling flu spread across the United States, we also apply our method to the Google Flu Trend data and report some very interesting epidemiological findings.
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