Bayesian Bootstraps for Massive Data

Recently, two scalable adaptations of the bootstrap have been proposed: the bag of little bootstraps (BLB; Kleiner et al., 2014) and the subsampled double bootstrap (SDB; Sengupta et al., 2016). In this paper, we introduce Bayesian bootstrap analogues to the BLB and SDB that have similar theoretical and computational properties, a strategy to perform lossless inference for a class of functionals of the Bayesian bootstrap, and briefly discuss extensions for Dirichlet Processes.