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

TL;DR

This paper introduces a distributed analysis method for massive data sets using generalized fiducial inference, enabling uncertainty quantification with minimal communication between nodes, suitable for privacy and efficiency concerns.

Contribution

It presents a novel divide-and-conquer approach with importance sampling for distributed generalized fiducial inference, providing uncertainty measures alongside point estimates.

Findings

Asymptotic equivalence to full data analysis

Minimal communication between nodes

Effective uncertainty quantification

Abstract

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