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.

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