Spatial direction vector data can be represented cylindrically by linear magnitudes and circular angles. We analyze such data by using a hierarchical Markov random field model with latent discrete classes and conditionally independent cylindrical data given the classes. The structure of a Potts model segments the spatial domain, and each class defines a cylindrical density that represents a specific structure. We consider two types of cylindrical distributions; the Weibull sine-skewed von Mises distribution, which is skewed in the circular part, and the generalized Pareto-type wrapped Cauchy distribution, which is heavy-tailed in the linear part. In this setting, we develop a statistically efficient block composite likelihood method for parameter estimation. The method is shown to provide much faster convergence than an expectation–maximization approach. However, the convergence is less stable for the block composite likelihood method, and we suggest a hybrid estimation approach for practical use. We apply the approach to study ocean surface currents in the Norwegian Sea. The models are able to describe the currents in terms of interpretable local regimes of two–three classes. Scoring rules are used to measure predictive performance of the two cylindrical densities. Results indicate that there is clearly skew angular components, and possibly also some heavy tails in magnitude.

空间方向矢量数据可以用线性幅度和圆角来表示。我们通过使用具有潜在离散类别的分层马尔可夫随机场模型和给定类别的条件独立圆柱数据来分析此类数据。Potts模型的结构分割了空间域，每个类别定义了代表特定结构的圆柱密度。我们考虑两种类型的圆柱分布；Weibull正弦形偏斜的von Mises分布（在圆形部分偏斜）和广义Pareto型包裹的Cauchy分布（在线性部分偏尾）。在这种情况下，我们开发了一种统计上有效的块组合似然方法，用于参数估计。与预期最大化方法相比，该方法可提供更快的收敛速度。但是，对于块组合似然法，收敛性较不稳定，因此我们建议使用混合估计法进行实际使用。我们应用该方法来研究挪威海中的海面洋流。这些模型能够用两到三类的可解释的地方制度来描述潮流。计分规则用于测量两个圆柱密度的预测性能。结果表明，明显存在倾斜的角度分量，并且可能还有数量级较大的尾巴。这些模型能够用两到三类的可解释的地方制度来描述潮流。计分规则用于测量两个圆柱密度的预测性能。结果表明，明显存在倾斜的角度分量，并且可能还有数量级较大的尾巴。这些模型能够用两到三类的可解释的地方制度来描述潮流。计分规则用于测量两个圆柱密度的预测性能。结果表明，明显存在倾斜的角度分量，并且可能还有数量级较大的尾巴。