Directional Asymmetry in Edge BasedSpatial Models via a Skew Normal Prior

TL;DR

This paper introduces a skew normal based spatial prior called RENeGe sk that captures directional asymmetry in edge-based spatial models, improving the modeling of asymmetric spatial patterns.

Contribution

The paper extends the Gaussian RENeGe framework by incorporating a skew normal distribution to model directional asymmetry, ensuring scalability and better edge-aligned structure recovery.

Findings

RENeGe sk more accurately recovers directional structures than Gaussian priors.

The model remains competitive under irregular spatial patterns.

Application demonstrates stable estimates with preserved directional variation.

Abstract

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.