Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009, Bilbao, Basque Country, Spain.
DIRO, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada.
Bull Math Biol. 2021 Jul 8;83(8):91. doi: 10.1007/s11538-021-00920-5.
We explore the use of Array-RQMC, a randomized quasi-Monte Carlo method designed for the simulation of Markov chains, to reduce the variance when simulating stochastic biological or chemical reaction networks with [Formula: see text]-leaping. The task is to estimate the expectation of a function of molecule copy numbers at a given future time T by the sample average over n sample paths, and the goal is to reduce the variance of this sample-average estimator. We find that when the method is properly applied, variance reductions by factors in the thousands can be obtained. These factors are much larger than those observed previously by other authors who tried RQMC methods for the same examples. Array-RQMC simulates an array of realizations of the Markov chain and requires a sorting function to reorder these chains according to their states, after each step. The choice of sorting function is a key ingredient for the efficiency of the method, although in our experiments, Array-RQMC was never worse than ordinary Monte Carlo, regardless of the sorting method. The expected number of reactions of each type per step also has an impact on the efficiency gain.
我们探索了使用 Array-RQMC，这是一种随机拟蒙特卡罗方法，专门用于模拟马尔可夫链，以减少使用 [Formula: see text]-leaping 模拟随机生物或化学反应网络时的方差。任务是通过 n 条样本路径的样本平均值来估计在给定未来时间 T 时分子拷贝数的函数的期望，目标是减少这个样本平均估计器的方差。我们发现，当正确应用该方法时，可以获得数千倍的方差减少。这些因子比其他作者之前尝试相同示例的 RQMC 方法观察到的因子大得多。Array-RQMC 模拟了马尔可夫链的一系列实现，并在每次步骤后需要一个排序函数根据状态对这些链进行重新排序。排序函数的选择是该方法效率的关键因素，尽管在我们的实验中，无论排序方法如何，Array-RQMC 从未比普通蒙特卡罗差。每种类型的反应在每一步的预期数量也会影响效率的提高。
