Directional data arise in various contexts such as oceanography (wave directions) and meteorology (wind directions), as well as with measurements on a periodic scale (weekdays, hours, etc.). Our contribution is to introduce a model-based approach to handle periodic data in the case of measurements taken at spatial locations, anticipating structured dependence between these measurements. We formulate a wrapped Gaussian spatial process model for this setting, induced from a customary linear Gaussian process.
We build a hierarchical model to handle this situation and show that the fitting of such a model is possible using standard Markov chain Monte Carlo methods. Our approach enables spatial interpolation (and can accommodate measurement error). We illustrate with a set of wave direction data from the Adriatic coast of Italy, generated through a complex computer model.
"Spatial analysis of wave direction data using wrapped Gaussian processes." Ann. Appl. Stat. 6 (4) 1478 - 1498, December 2012. https://doi.org/10.1214/12-AOAS576