Title: Non-stationary wrapped Gaussian processes with sparse precision matrices
Authors: Thomas Kneib - University of Goettingen (Germany)
Nadja Klein - Humboldt University Berlin (Germany)
Isa Marques - University of Goettingen (Germany) [presenting]
Abstract: Directional data, i.e., data consisting of angles, can be found across many areas of science, such ecology, biology, environmental sciences, or medicine. The special nature of such data means that conventional methods for linear data are not suitable. Nonetheless, few attempts have been made to develop flexible models for periodic data, namely spatial models. Gaussian random fields are one of the most important building blocks for hierarchical models for spatial data. Yet the need to factorize dense covariance matrices renders them quite computationally expensive. We introduce a spatial model for wrapped Gaussian data which, given the empirical equivalence between Gaussian and Gaussian Markov random fields, considerably reduces computational complexity by using sparse matrix algorithms. The selection of appropriate hyperpriors for the Gaussian fields' parameters is an important and sensible topic, specially given that these are not consistently estimable from a single realization. Consequently, we develop penalized complexity priors for the model's hyperparameters that are practically useful and tunable. The posterior distribution is assessed with an adaptive Markov chain Monte Carlo. Finally, we extend previously existing directional data models by allowing for covariates in both the mean and the covariance structure, as well as for a nugget effect.