Bayesian functional prediction of excursion sets for Gaussian spatiotemporal random fields

M. D. Ruiz-Medina, A. E. Madrid, J. M. Angulo, A. Torres-Signes

An empirical Bayesian functional regression approach is adopted to approximate the asymptotic predictive probability distribution of the volume of excursion sets of spherical Gaussian Spatiotemporal Random Fields. Estimation results are derived covering the cases of fixed and moving levels. The methodological approach presented is implemented from samples of temporal correlated spherical functional data affected by additive spatiotemporal spherical Gaussian noise. In particular, an infinite-dimensional version of Gaussian Process Regression is obtained, covering the cases of weak- and strong-dependent functional data. Results are illustrated via simulations and real-data applications, considering the family of spatiotemporal covariance functions in the Gneiting class

Keywords: Time-adaptive Empirical Bayes, excursion sets, functional Gaussian Process Regression, time correlated functional data

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