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A hierarchical spatiotemporal statistical model motivated by glaciology. (English) Zbl 1427.86011

Summary: In this paper, we extend and analyze a Bayesian hierarchical spatiotemporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.

MSC:

86A32 Geostatistics
62F15 Bayesian inference
62P12 Applications of statistics to environmental and related topics
86A30 Geodesy, mapping problems
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