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.

翻译：柱面数据广泛出现于多个科学领域，包括气象学（如风向与风速）、海洋学（如海流方向与流速或波高）、生态学（如生物遥测）以及医学（如疾病发病的季节性与强度）。此类数据常呈现为空间相关的强度与角度序列，从而构成兼具线性分量与圆周分量的相依二元响应向量。为同时适应圆周-线性相依性与空间自相关性，并在边缘分布设定上保持灵活性，文献中已发展出基于Copula的柱面数据模型。然而，现有方法通常将Copula参数视为与协变量无关的常数，且边缘分布的回归设定常局限于线性预测变量，从而忽略了空间相关性。本研究提出一种结构化加性条件Copula回归模型用于柱面数据分析。其中圆周分量采用环绕高斯过程建模，线性分量遵循分布回归模型。两个分量均允许纳入线性协变量效应。此外，通过利用高斯随机场与高斯马尔可夫随机场之间的经验等价性，本方法避免了高斯随机场通常伴随的计算负担，同时允许协方差结构存在非平稳性。后验估计通过马尔可夫链蒙特卡洛模拟实现。我们通过模拟研究及对德国风向与风速数据的分析，对所提模型进行了评估。