In the era of Big Data, Markov chain Monte Carlo (MCMC) methods, which are currently essential for Bayesian estimation, face significant computational challenges owing to their sequential nature. To achieve a faster and more effective parallel computation, we emphasize the critical role of the overlapped area of the posterior distributions based on partitioned data, which we term the reconstructable area. We propose a method that utilizes machine learning classifiers to effectively identify and extract MCMC draws obtained by parallel computations from the area based on posteriors based on partitioned sub-datasets, approximating the target posterior distribution based on the full dataset. This study also develops a Kullback-Leibler (KL) divergence-based criterion. It does not require calculating the full-posterior density and can be calculated using only information from the sub-posterior densities, which are generally obtained after implementing MCMC. This simplifies the hyperparameter tuning in training classifiers. The simulation studies validated the efficacy of the proposed method. This approach contributes to ongoing research on parallelizing MCMC methods and may offer insights for future developments in Bayesian computation for large-scale data analyses.

翻译：在大数据时代，马尔可夫链蒙特卡洛（MCMC）方法作为当前贝叶斯估计的核心工具，因其固有的序列特性而面临显著的计算挑战。为实现更快速、更高效的并行计算，我们强调基于分区数据的后验分布重叠区域——我们称之为可重构区域——的关键作用。我们提出一种方法，利用机器学习分类器有效地识别并提取通过并行计算从基于分区子数据集的后验分布中获得的MCMC样本，从而近似基于完整数据集的目标后验分布。本研究还发展了一种基于Kullback-Leibler（KL）散度的准则。该准则无需计算完整后验密度，仅利用子后验密度信息（通常在执行MCMC后获得）即可计算，从而简化了分类器训练中的超参数调优。模拟研究验证了所提方法的有效性。该方法为MCMC方法的并行化研究提供了新的思路，并可能为未来大规模数据分析的贝叶斯计算发展带来启示。