Markov chain Monte Carlo (MCMC) is a popular and successful general-purpose tool for Bayesian inference. However, MCMC cannot be practically applied to large data sets because of the prohibitive cost of evaluating every likelihood term at every iteration. Here we present Firefly Monte Carlo (FlyMC) an auxiliary variable MCMC algorithm that only queries the likelihoods of a potentially small subset of the data at each iteration yet simulates from the exact posterior distribution, in contrast to recent proposals that are approximate even in the asymptotic limit. FlyMC is compatible with a wide variety of modern MCMC algorithms, and only requires a lower bound on the per-datum likelihood factors. In experiments, we find that FlyMC generates samples from the posterior more than an order of magnitude faster than regular MCMC, opening up MCMC methods to larger datasets than were previously considered feasible.

本文讲述了一种名为Firefly Monte Carlo (FlyMC)的辅助变量MCMC算法，它只在每次迭代中查询可能较小子集的数据似然，而不像最近的提议一样，即使在渐近极限下也是近似的。实验表明，FlyMC生成的后验样本比常规MCMC快一个以上数量级，从而将MCMC方法应用于先前认为不可行的更大数据集。

萤火莫尔卡罗: 子数据精确MCMC