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Spatio-temporal circular models with non-separable covariance structure

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Abstract

Circular data arise in many areas of application. Recently, there has been interest in looking at circular data collected separately over time and over space. Here, we extend some of this work to the spatio-temporal setting, introducing space–time dependence. We accommodate covariates, implement full kriging and forecasting, and also allow for a nugget which can be time dependent. We work within a Bayesian framework, introducing suitable latent variables to facilitate Markov chain Monte Carlo model fitting. The Bayesian framework enables us to implement full inference, obtaining predictive distributions for kriging and forecasting. We offer comparison between the less flexible but more interpretable wrapped Gaussian process and the more flexible but less interpretable projected Gaussian process. We do this illustratively using both simulated data and data from computer model output for wave directions in the Adriatic Sea off the coast of Italy.

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Acknowledgments

The authors thank INFN Bari CED for allowing the use of their high-performance grid computing infrastructure Bc2S. The authors thank ISPRA for the use of data output from the wave model of its SIMM hydro-meteo-marine forecasting system.

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Correspondence to Gianluca Mastrantonio.

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Mastrantonio, G., Jona Lasinio, G. & Gelfand, A.E. Spatio-temporal circular models with non-separable covariance structure. TEST 25, 331–350 (2016). https://doi.org/10.1007/s11749-015-0458-y

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  • DOI: https://doi.org/10.1007/s11749-015-0458-y

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