Abstract:
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Spatial process models provide a rich framework for modeling dependence in response arising from a variety of scientific domains. Analyzing topological properties of the resulting surface generated through such modeling provides a deeper insight into the nature of latent dependence within the studied response. Such analyses naturally require constraints on the smoothness of the surface, which primarily depends on the analytic properties of the chosen kernel. The literature contains inference on quantities of interest, for example, first-order properties like gradients and aspects, which indicate a rate of change and direction associated with the maximum rate of change. This manuscript provides a model-based framework for inferring on second-order properties specifying curvature for the latent surface, it also derives necessary conditions on the smoothness of kernels required for studying curvature. Inferential framework is developed for mean and Gaussian curvature and, the first and second fundamental form which are common differential geometric notions associated with a smooth surface.
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