A non-stationary model for spatially dependent circular response data based on wrapped Gaussian processes

Marques, I., Kneib, T. and Klein, N. (2022) A non-stationary model for spatially dependent circular response data based on wrapped Gaussian processes. Statistics and Computing, 32(5), 73. (doi: 10.1007/s11222-022-10136-9)

Abstract

Circular data can be found across many areas of science, for instance meteorology (e.g., wind directions), ecology (e.g., animal movement directions), or medicine (e.g., seasonality in disease onset). The special nature of these data means that conventional methods for non-periodic data are no longer valid. In this paper, we consider wrapped Gaussian processes and introduce a spatial model for circular data that allow for non-stationarity in the mean and the covariance structure of Gaussian random fields. We use the empirical equivalence between Gaussian random fields and Gaussian Markov random fields which allows us to considerably reduce computational complexity by exploiting the sparseness of the precision matrix of the associated Gaussian Markov random field. Furthermore, we develop tunable priors, inspired by the penalized complexity prior framework, that shrink the model toward a less flexible base model with stationary mean and covariance function. Posterior estimation is done via Markov chain Monte Carlo simulation. The performance of the model is evaluated in a simulation study. Finally, the model is applied to analyzing wind directions in Germany.

• Item Type: Articles
• Additional Information: Open Access funding enabled and organized by Projekt DEAL. The authors gratefully acknowledge the Deutsche Forschungsgemeinschaft for funding the project within the Research Training Group 2300 “Enrichment of European beech forests with conifers”.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Marques, Dr Isa
• Authors: Marques, I., Kneib, T., and Klein, N.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Statistics and Computing
• Publisher: Springer
• ISSN: 0960-3174
• ISSN (Online): 1573-1375
• Published Online: 03 September 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Statistics and Computing 32(5):73
• Publisher Policy: Reproduced under a Creative Commons License