Copula-based models for spatially dependent cylindrical data

2026-02-05

AI Summary

This study addresses the challenge of jointly modeling linear and circular components in spatially correlated cylindrical data, where existing approaches struggle to simultaneously accommodate covariate dependence, flexible marginal distributions, and spatial autocorrelation. The authors propose a structured additive conditional copula regression model that employs a covariate-driven wrapped Gaussian process for the circular component and distributional regression for the linear component. Notably, the model incorporates nonstationary spatial random effects into the copula parameterization—a novel extension that overcomes the conventional limitations of constant copula parameters and linear marginal regressions. Bayesian inference via MCMC is implemented, leveraging the equivalence between Gaussian random fields and Gaussian Markov random fields to enhance computational efficiency. Both simulation studies and an empirical analysis of wind speed and direction data from Germany demonstrate the model’s superior performance in terms of both fitting accuracy and computational scalability.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: User model development and evaluation
• Web Mining and Content Analysis: Bridging structured and unstructured data

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.

Problem

• cylindrical data
• spatial dependence
• copula models
• regression
• non-stationarity

Innovation

• copula regression
• cylindrical data
• wrapped Gaussian process
• Gaussian Markov random field
• spatial non-stationarity