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It is not unusual for a data analyst to encounter data sets distributedacross several computers. This can happen for reasons such as privacy concerns,efficiency of likelihood evaluations, or just the sheer size of the whole dataset. This presents new challenges to statisticians as even computing simplesummary statistics such as the median becomes computationally challenging.Furthermore, if other advanced statistical methods are desired, novelcomputational strategies are needed. In this paper we propose a new approachfor distributed analysis of massive data that is suitable for generalizedfiducial inference and is based on a careful implementation of a "divide andconquer" strategy combined with importance sampling. The proposed approachrequires only small amount of communication between nodes, and is shown to beasymptotically equivalent to using the whole data set. Unlike most existingmethods, the proposed approach produces uncertainty measures (such asconfidence intervals) in addition to point estimates for parameters ofinterest. The proposed approach is also applied to the analysis of a large setof solar images.

Method G: Uncertainty Quantification for Distributed Data Problems using Generalized Fiducial Inference