# Bayesian Bootstraps for Massive Data

## TL;DR

This paper introduces scalable algorithms for the Bayesian bootstrap that enable approximate inference on massive datasets, drawing parallels with frequentist methods and extending to lossless inference and Dirichlet Process extensions.

## Contribution

It proposes data-subsetting algorithms for Bayesian bootstrap that are scalable and theoretically sound, and introduces methods for lossless inference and Dirichlet Process extensions.

## Key findings

- Algorithms are computationally efficient for large data
- Theoretical properties match those of frequentist counterparts
- Extensions to Dirichlet Process are briefly discussed

## Abstract

In this article, we present data-subsetting algorithms that allow for the approximate and scalable implementation of the Bayesian bootstrap. They are analogous to two existing algorithms in the frequentist literature: the bag of little bootstraps (Kleiner et al., 2014) and the subsampled double bootstrap (SDB; Sengupta et al., 2016). Our algorithms have appealing theoretical and computational properties that are comparable to those of their frequentist counterparts. Additionally, we provide a strategy for performing lossless inference for a class of functionals of the Bayesian bootstrap, and briefly introduce extensions to the Dirichlet Process.