Models for space-time directional data using Wrapped Gaussian processes

In the present work we review modeling strategies based on wrapped Gaussian processes defined to model directional spatio-temporal data. We first il- lustrate the model-based approach to handle spatial periodic data. The wrapped Gaussian spatial process is here induced by a customary linear Gaussian process. We formulate the model as a Bayesian hierarchical one and we show that the fit- ting of the model is possible using standard Markov chain Monte Carlo methods. Then we move to some spatio-temporal generalizations of the spatial model. In the spatio-temporal setting we present a simulation study of our proposal aiming at un- derstanding its computational and statistical properties. We highlight the pros and cons of this model and the difficulties arising in the implementation of the MCMCs. Eventually we provide some general advice in the use of spatio-temporal wrapped Gaussian process and we provide a real data example