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Variance Reduction with Array-RQMC for Tau-Leaping Simulation of Stochastic Biological and Chemical Reaction Networks
Bulletin of Mathematical Biology ( IF 3.5 ) Pub Date : 2021-07-08 , DOI: 10.1007/s11538-021-00920-5
Florian Puchhammer 1, 2 , Amal Ben Abdellah 2 , Pierre L'Ecuyer 2
Affiliation  

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 \(\tau \)-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.



中文翻译:

使用 Array-RQMC 减少随机生物和化学反应网络的 Tau 跳跃模拟的方差

我们探索使用 Array-RQMC,一种设计用于模拟马尔可夫链的随机准蒙特卡罗方法,以减少在模拟具有\(\tau \)跳跃的随机生物或化学反应网络时的方差。任务是通过n上的样本平均值来估计给定未来时间T的分子拷贝数函数的期望值样本路径,目标是减少该样本平均估计量的方差。我们发现,当正确应用该方法时,可以获得数千个因子的方差减少。这些因素远大于其他作者之前对相同示例尝试 RQMC 方法所观察到的因素。Array-RQMC 模拟马尔可夫链的一系列实现,并且需要一个排序函数在每一步之后根据它们的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 从未比普通的 Monte Carlo 差。每个步骤的每种类型的预期反应数量也对效率增益有影响。

更新日期:2021-07-08
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