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Statistica Sinica 25 (2015), 25-39

JOINT SPATIO-TEMPORAL ANALYSIS OF A LINEAR AND
A DIRECTIONAL VARIABLE: SPACE-TIME MODELING
OF WAVE HEIGHTS AND WAVE DIRECTIONS IN
THE ADRIATIC SEA
Fangpo Wang1, Alan E. Gelfand1 and Giovanna Jona-Lasinio2
1Duke University and 2University of Rome Sapienza

Abstract: It is valuable to have a better understanding of factors that influence sea motion and to provide more accurate forecasts. In particular, we are motivated by data on wave heights and outgoing wave directions over a region in the Adriatic sea during the time of a storm, with the overarching goal of understanding the association between wave directions and wave heights to enable improved prediction of wave behavior. Our contribution is to develop a fully model-based approach to capture joint structured spatial and temporal dependence between a linear and an angular variable. Model fitting is carried out using a suitable data augmented Markov chain Monte Carlo (MCMC) algorithm. We illustrate with data outputs from a deterministic wave model for a region in the Adriatic Sea. The proposed joint model framework enables both spatial interpolation and temporal forecasting.

Key words and phrases: Angular variable, Bayesian kriging, hierarchical model, latent variables, Markov chain Monte Carlo, projected Gaussian process, significant wave height.

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