Abstract

Speeding up Markov chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators, allowing us to update a single block of subsample indicators in each MCMC iteration so that a desired correlation is achieved between the logs of successive likelihood estimates. This is important since pseudo-marginal MCMC with positively correlated likelihood estimates can use substantially smaller subsamples without adversely affecting the sampling efficiency. The block-Poisson estimator is unbiased but not necessarily positive, so the algorithm runs the MCMC on the absolute value of the likelihood estimator and uses an importance sampling correction to obtain consistent estimates of the posterior mean of any function of the parameters. Our article derives guidelines to select the optimal tuning parameters for our method and shows that it compares very favorably to regular MCMC without subsampling, and to two other recently proposed exact subsampling approaches in the literature. Supplementary materials for this article are available online.

摘要

通过数据子采样为具有许多观察结果的数据集加速马尔可夫链蒙特卡罗（MCMC）最近受到了相当多的关注。提出了一种伪边际 MCMC 方法，该方法使用块泊松估计器通过数据子采样来估计似然。估计量是泊松估计量的产物，允许我们在每次 MCMC 迭代中更新单个子样本指标块，以便在连续似然估计的对数之间实现所需的相关性。这很重要，因为具有正相关似然估计的伪边际 MCMC 可以使用显着更小的子样本，而不会对采样效率产生不利影响。块泊松估计量是无偏的，但不一定是正的，因此，该算法在似然估计量的绝对值上运行 MCMC，并使用重要性采样校正来获得参数任何函数的后验均值的一致估计。我们的文章得出了为我们的方法选择最佳调整参数的指南，并表明它与没有二次采样的常规 MCMC 以及最近在文献中提出的另外两种精确二次采样方法相比非常有利。本文的补充材料可在线获取。以及最近在文献中提出的另外两种精确子采样方法。本文的补充材料可在线获取。以及最近在文献中提出的另外两种精确子采样方法。本文的补充材料可在线获取。