Seminar at SMU Delhi

Circular data arise in oceanography (wave directions) and meteorology (wind directions), and, more generally, with periodic measurements recorded in degrees or angles on a circle. In this talk we introduce a fully model-based approach to handle circular 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 {\em inline} Gaussian process. We look at the properties of this process, including the induced correlation structure. We build a hierarchical model to handle this situation and show how to fit this model straightforwardly using Markov chain Monte Carlo methods. Our approach enables spatial interpolation and can accommodate measurement error. We illustrate with a set of angular wave direction data from the Adriatic coast of Italy, generated through a complex computer model. Then, we consider the projected normal spatial process built from a bivariate Gaussian process model. Such models are more flexible than usual wrapped or von Mises models and easily handle regression. However, they are more challenging to fit. We illustrate with a butterfly dataset.