Directional Asymmetry in Edge‐Based Spatial Models via a Skew–Normal Prior

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‐align 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.