Title: Bayesian Bootstraps for Massive Data,
Abstract: 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.