This paper introduces a class of Monte Carlo algorithms which are based on the simulation of a Markov process whose quasi‐stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current Markov chain Monte Carlo methods which simulate a Markov chain whose stationary distribution is the target. We show how to approximate distributions of interest by carefully combining sequential Monte Carlo methods with methodology for the exact simulation of diffusions. The methodology introduced here is particularly promising in that it is applicable to the same class of problems as gradient‐based Markov chain Monte Carlo algorithms but entirely circumvents the need to conduct Metropolis–Hastings type accept–reject steps while retaining exactness: the paper gives theoretical guarantees ensuring that the algorithm has the correct limiting target distribution. Furthermore, this methodology is highly amenable to ‘big data’ problems. By employing a modification to existing naive subsampling and control variate techniques it is possible to obtain an algorithm which is still exact but has sublinear iterative cost as a function of data size.

中文翻译：

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准平稳蒙特卡罗和ScaLE算法

本文介绍了一类基于蒙特卡罗算法的蒙特卡罗算法，该算法的拟平稳分布与目标分布相吻合。这与当前的马尔可夫链蒙特卡罗方法根本不同，该方法模拟了以平稳分布为目标的马尔可夫链。我们展示了如何通过仔细地将顺序蒙特卡罗方法与用于扩散的精确模拟的方法学仔细结合起来，来近似估计感兴趣的分布。这里介绍的方法特别有希望，因为它适用于与基于梯度的马尔可夫链蒙特卡罗算法相同的问题类别，但完全避免了在保持准确性的情况下进行Metropolis-Hastings类型的接受-拒绝步骤的需要：本文提供了理论上的保证，以确保算法具有正确的极限目标分布。此外，这种方法非常适合“大数据”问题。通过对现有的朴素的二次采样和控制变量技术进行修改，可以获得一种算法，该算法仍然是精确的，但是具有亚线性迭代成本作为数据大小的函数。