Temporal and spatio-temporal modes for circular and circular-linear data

Abstract

Circular data arise naturally in many scientific fields, for example oceanography (wave directions), meteorology (wind directions), biology (animal movement). Due to the circular domain, to the sensitivity of descriptive and inferential results to the starting point and orientation on the circle, analysis of circular data is challenging. We propose models for temporal and spatio-temporal circular and circular-linear data. We show that under a Bayesian framework, the complex nature of circular data and the difficulties in a joint modelling of circular-linear variables can be easily overcome. Two main research frameworks are touched. The first deals with the build of spatio-temporal models for circular variables, while the second address topics in the joint temporal classification of circular-linear variables. In all the models proposed, exploiting data augmentation techniques, we are able to propose efficient, and easy to implement, Markov chain Monte Carlo algorithm.