This paper proposes a simple, practical, and efficient MCMC algorithm for Bayesian analysis of big data. The proposed algorithm suggests to divide the big dataset into some smaller subsets and provides a simple method to aggregate the subset posteriors to approximate the full data posterior. To further speed up computation, the proposed algorithm employs the population stochastic approximation Monte Carlo algorithm, a parallel MCMC algorithm, to simulate from each subset posterior. Since this algorithm consists of two levels of parallel, data parallel and simulation parallel, it is coined as “Double-Parallel Monte Carlo.” The validity of the proposed algorithm is justified mathematically and numerically.

中文翻译：

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贝叶斯大数据贝叶斯分析的双重并行蒙特卡洛方法。

本文提出了一种简单，实用，高效的MCMC算法用于大数据的贝叶斯分析。提出的算法建议将大数据集划分为一些较小的子集，并提供一种简单的方法来聚合子集后代以近似整个数据后验。为了进一步加快计算速度，该算法采用了种群随机逼近蒙特卡罗算法（一种并行的MCMC算法）来对每个子集后验进行仿真。由于该算法由并行，数据并行和模拟并行两个级别组成，因此被称为“双并行蒙特卡洛”。该算法的有效性在数学和数值上得到了证明。