Abstract:
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Despite its wide variety of applications in different scientific disciplines, such as geophysical, environmental and social sciences, the study of a random process on a network is a relative new area in geostatistics. The covariance function of such a stochastic process captures the small-scale variation over space-time in a parsimonious way and plays a central role in prediction and regression-type parameter estimation involving different types of networks in application, e.g. traffic networks, stream networks, computer networks, social networks, etc. Although a broad range of classes of space-time covariance models are available in Euclidean space, the corresponding results for pure spatial linear networks are few and far between, not to mention temporal networks. To fill in the gaps, we develop parametric covariance functions on temporal networks assuming that the underlying network structure doesn't evolve over time, using a Hilbert space embedding technique and a kernel convolution-based approach. We evaluate the model performance on the daily stream temperature data set from the north-western United States.
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