The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets. Data subsampling has recently been suggested as a way to make MCMC methods scalable on massively large data, utilizing efficient sampling schemes and estimators from the survey sampling literature. These developments tend to be unknown by many survey statisticians who traditionally work with non-Bayesian methods, and rarely use MCMC. Our article explains the idea of data subsampling in MCMC by reviewing one strand of work, Subsampling MCMC, a so called pseudo-marginal MCMC approach to speeding up MCMC through data subsampling. The review is written for a survey statistician without previous knowledge of MCMC methods since our aim is to motivate survey sampling experts to contribute to the growing Subsampling MCMC literature.
Spectral subsampling MCMC for Lévy-driven continuous-time ARMA models with expensive likelihood contributions
Human Technology Institute, University of Technology Sydney（悉尼科技大学人类技术研究所）；School of Mathematical and Physical Sciences, University of Technology Sydney（悉尼科技大学数理科学学院）；School of Economics, University of New South Wales（新南威尔士大学经济管理学院）；Guanghua School of Management, Peking University（北京大学光华管理学院）
Improving Sampling Accuracy of Stochastic Gradient MCMC Methods via Non-uniform Subsampling of Gradients
Georgia Institute of Technology（佐治亚理工学院）；Google Inc.（谷歌公司）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
许多马尔可夫链蒙特卡罗（MCMC）方法利用目标分布的势函数的梯度信息来有效地探索样本空间。然而，计算梯度对于大规模应用（诸如当代机器学习中的那些应用）而言通常在计算上是昂贵的。随机梯度（SG-）MCMC方法通常通过均匀子采样的数据点通过随机梯度来近似梯度，并且实现了提高的计算效率，但是以引入采样误差为代价。我们提出了一种非均匀子采样方案，以提高采样精度。提出的指数加权随机梯度（EWSG）的设计，使一个非均匀SG-MCMC方法模仿的批量梯度MCMC方法的统计行为，因此，由于SG近似的不准确性减少。EWSG不同于经典的方差缩减（VR）技术，因为它关注的是整个分布而不仅仅是方差;尽管如此，它的局部方差也被证明了。EWSG也可以被看作是重要性采样思想的扩展，成功的随机梯度为基础的优化，采样任务。在EWSG的实际实现中，非均匀子采样通过数据索引上的Metropolis-Hastings链有效地执行，该链与MCMC算法耦合。数值实验不仅证明了EWSG的有效性，而且还指导超参数的选择，并验证我们的\emph{non-asymptotic global error bound}，尽管在实现中的近似。值得注意的是，虽然统计精度得到了提高，但收敛速度可以与统一版本相媲美，这使得EWSG成为VR的实用替代方案（但EWSG和VR也可以组合）。
Stabilised weighted data subsampling for accelerated Bayesian inference in models with recursive likelihoods
University of Technology Sydney（悉尼科技大学）；University of New South Wales（新南威尔士大学）；Human Technology Institute, University of Technology Sydney（悉尼科技大学人类技术研究所）
Bayesian neural networks via MCMC: a Python-based tutorial
School of Mathematics and Statistics, UNSW Sydney（新南威尔士大学悉尼分校数学与统计学院）；Pingala Institute of Artificial Intelligence（平加拉人工智能研究院）；University of Sydney（悉尼大学）
University of Halmstad（哈尔姆斯塔德大学）；Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所 HIIT）；University of Helsinki（赫尔辛基大学）；Aalto University（阿尔托大学）
