Copula-based models for spatially dependent cylindrical data

TL;DR

This paper introduces a flexible copula-based regression model for spatially dependent cylindrical data, capturing circular-linear dependence and spatial autocorrelation with non-stationary covariance structures.

Contribution

It develops a structured additive model using wrapped Gaussian processes and distributional regression, addressing limitations of existing methods by incorporating covariate-dependent copula parameters.

Findings

Model effectively captures spatial dependence in wind data.

Simulation studies demonstrate improved flexibility and accuracy.

Application to German wind data shows practical utility.

Abstract

Cylindrical data frequently arise across various scientific disciplines, including meteorology (e.g., wind direction and speed), oceanography (e.g., marine current direction and speed or wave heights), ecology (e.g., telemetry), and medicine (e.g., seasonality and intensity in disease onset). Such data often occur as spatially correlated series of intensities and angles, thereby representing dependent bivariate response vectors of linear and circular components. To accommodate both the circular-linear dependence and spatial autocorrelation, while remaining flexible in marginal specifications, copula-based models for cylindrical data have been developed in the literature. However, existing approaches typically treat the copula parameters as constants unrelated to covariates, and regression specifications for marginal distributions are frequently restricted to linear predictors, thereby ignoring spatial correlation. In this work, we propose a structured additive conditional copula regression model for cylindrical data. The circular component is modeled using a wrapped Gaussian process, and the linear component follows a distributional regression model. Both components allow for the inclusion of linear covariate effects. Furthermore, by leveraging the empirical equivalence between Gaussian random fields (GRFs) and Gaussian Markov random fields, our approach avoids the computational burden typically associated with GRFs, while simultaneously allowing for non-stationarity in the covariance structure. Posterior estimation is performed via Markov chain Monte Carlo simulation. We evaluate the proposed model in a simulation study and subsequently in an analysis of wind directions and speed in Germany.