Motivated by the need for computationally tractable spatial methods in neuroimaging studies, we develop a distributed and integrated framework for estimation and inference of Gaussian process model parameters with ultra-high-dimensional likelihoods. We propose a shift in viewpoint from whole to local data perspectives that is rooted in distributed model building and integrated estimation and inference. The framework's backbone is a computationally and statistically efficient integration procedure that simultaneously incorporates dependence within and between spatial resolutions in a recursively partitioned spatial domain. Statistical and computational properties of our distributed approach are investigated theoretically and in simulations. The proposed approach is used to extract new insights on autism spectrum disorder from the Autism Brain Imaging Data Exchange.

翻译：受神经影像研究中计算可行性空间方法的需求驱动，我们开发了一种分布式集成框架，用于超高维似然函数下高斯过程模型参数的估计与推断。我们提出从全局数据视角向局部数据视角的转变，其核心思想植根于分布式模型构建与集成式估计推断。该框架的支柱是一种兼具计算效率与统计效能的整合程序，能够在递归分割的空间域内同时整合空间分辨率内部及不同分辨率之间的依赖关系。我们通过理论推导和仿真实验研究了分布式方法的统计特性与计算性能。利用所提方法，我们从自闭症脑成像数据交换库中提取出关于自闭症谱系障碍的新见解。