This paper aims to extend the Besag model, a widely used Bayesian spatial model in disease mapping, to a non-stationary spatial model for irregular lattice-type data. The goal is to improve the model's ability to capture complex spatial dependence patterns and increase interpretability. The proposed model uses multiple precision parameters, accounting for different intensities of spatial dependence in different sub-regions. We derive a joint penalized complexity prior for the flexible local precision parameters to prevent overfitting and ensure contraction to the stationary model at a user-defined rate. The proposed methodology can be used as a basis for the development of various other non-stationary effects over other domains such as time. An accompanying R package 'fbesag' equips the reader with the necessary tools for immediate use and application. We illustrate the novelty of the proposal by modeling the risk of dengue in Brazil, where the stationary spatial assumption fails and interesting risk profiles are estimated when accounting for spatial non-stationary.

翻译：本文旨在将疾病制图中广泛使用的贝叶斯空间模型——Besag模型扩展为适用于不规则格点数据的非平稳空间模型。研究目标在于提升模型捕捉复杂空间依赖模式的能力并增强可解释性。所提出的模型通过引入多个精度参数，刻画不同子区域中空间依赖强度的差异性。我们为灵活局部精度参数推导了联合惩罚复杂度先验，以防止过拟合，并确保以用户定义的速率收缩至平稳模型。该建模方法可作为开发时间等其他领域非平稳效应的理论框架。配套R包'fbesag'为读者提供即时应用所需的工具。我们通过建模巴西登革热风险验证了本方法的创新性——在平稳空间假设失效的情况下，通过纳入空间非平稳性估计出了具有显著特征的风险剖面。