Motivated by a high-dimensional regression problem in spatial multimodal omics (SMO), we propose a Bayesian framework for local spatial feature selection, where a random domain partition prior is introduced to divide the spatial domain into several contiguous clusters with flexible shapes and an unknown number of clusters, conditional on which a local feature selection prior is imposed within each cluster. The notion of "feature" is general and may include both covariates and functional bases, allowing the framework to perform both local variable selection and local basis selection, the latter being essential for adaptively approximating spatially varying functions with localized characteristics. We derive coupled hyperparameter conditions linking domain partition and local feature selection priors, under which the consistency theory and posterior contraction rates of both the domain partition and feature selection are established. We develop an efficient informed reversible jump Markov chain Monte Carlo algorithm to address the computational challenges encountered in joint posterior sampling of domain partitions and selected features. Simulation studies demonstrate the effectiveness of the proposed model and algorithm, highlighting its advantages over existing methods. The application of our model to an SMO dataset reveals biologically meaningful spatial patterns within breast cancer tissue.

翻译：受空间多模态组学（SMO）中高维回归问题的启发，我们提出了一种用于局部空间特征选择的贝叶斯框架。该框架引入随机域划分先验，将空间域划分为若干具有灵活形状且数量未知的连续簇，并在每个簇内施加局部特征选择先验。"特征"的概念具有一般性，可涵盖协变量与函数基，使得该框架既能执行局部变量选择，又能执行局部基选择——后者对于自适应逼近具有局部特性的空间变函数至关重要。我们推导了连接域划分与局部特征选择先验的耦合超参数条件，在此基础上建立了域划分与特征选择的一致性理论及后验收缩速率。为应对域划分与所选特征联合后验采样中的计算挑战，我们开发了一种高效的信息化可逆跳跃马尔可夫链蒙特卡洛算法。模拟研究验证了所提模型与算法的有效性，凸显其相较于现有方法的优势。将该模型应用于SMO数据集后，揭示了乳腺癌组织中具有生物学意义的空间模式。