Motivated by the important need for computationally tractable statistical methods in high dimensional spatial settings, we develop a distributed and integrated framework for estimation and inference of Gaussian model parameters with ultra-high-dimensional likelihoods. We propose a paradigm shift 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：受高维空间场景下对可计算统计方法的迫切需求驱动，我们针对超高维高斯模型参数的估计与推断问题，提出了一种分布式与集成化框架。该方法突破传统全局数据视角，建立于分布式模型构建与集成式估计及推断的范式之上。该框架的核心在于一种兼具计算与统计高效性的集成过程，该过程在递归划分的空间域中同步整合空间分辨率内部及跨分辨率间的依赖性。我们从理论和仿真层面系统研究了所提分布式方法的统计与计算特性。通过将所提方法应用于自闭症脑成像数据交换库，本研究为自闭症谱系障碍提供了新的洞察。