We introduce a skewed edge based spatial prior, named RENeGe sk that extends the Gaussian RENeGe framework by incorporating directional asymmetry through a skew normal distribution. Skewness is defined on the edge graph and propagated to the node space, aligning asymmetric behavior with transitions across neighboring regions rather than with marginal node effects. The model is formulated within the skew normal framework and employs identifiable hierarchical priors together with low rank parameterizations to ensure scalability. The skew normal's stochastic representation is considered to facilitate the computational implementation. Simulation studies show that RENeGe sk recovers compact, edge-aligned directional structure more accurately than symmetric Gaussian priors, while remaining competitive under irregular spatial patterns. An application to cancer incidence data in Southern Brazil illustrates how the proposed approach yields stable area-level estimates while preserving localized, directionally driven spatial variation.

翻译：本文提出了一种名为RENeGe sk的偏斜边缘空间先验，该先验通过引入偏斜正态分布来扩展高斯RENeGe框架，从而纳入方向性不对称性。偏斜性定义在边缘图上并传播到节点空间，使得不对称行为与相邻区域间的转移过程对齐，而非与节点的边际效应相关联。该模型在偏斜正态框架内构建，采用可识别的分层先验并结合低秩参数化以确保可扩展性。文中考虑了偏斜正态的随机表示以促进计算实现。模拟研究表明，与对称高斯先验相比，RENeGe sk能更准确地恢复紧凑且与边缘对齐的方向性结构，同时在非规则空间模式下仍保持竞争力。通过对巴西南部癌症发病率数据的应用，展示了所提方法如何在保持局部、方向驱动的空间变异的同时，获得稳定的区域级估计。