Quasi-Monte Carlo Methods Applied to Tau-Leaping in Stochastic Biological Systems.
Quasi-Monte Carlo Methods Applied to Tau-Leaping in Stochastic Biological Systems.
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DOI：
10.1007/s11538-018-0442-2
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发表时间：
2019-08
影响因子：
3.5
通讯作者：
Baker RE
中科院分区：
文献类型：
--
作者：
Beentjes CHL;Baker RE
拟蒙特卡罗方法已被证明是传统蒙特卡罗方法的有效扩展，其中包括正交问题和随机微分方程的样本路径模拟。通过用低差异数输入流代替模拟过程中的随机数输入流，在金融应用中观察到几个数量级的方差减少。混合良好的化学反应网络中的随机效应分析通常依赖于使用蒙特卡罗方法的样本路径模拟，尽管这些方法具有典型的慢收敛速度（作为样本路径n的函数）。本文研究了（随机）准蒙特卡罗方法与有效的样本路径模拟过程（即-跳跃）的结合。我们表明，就统计误差的衰减而言，这种组合通常比传统的蒙特卡罗模拟更有效。然而，由于化学反应模型的离散性，观察到的收敛速率行为是不平凡的。我们通过观察标准正交中的一个测试问题来解释这如何影响准蒙特卡罗方法的性能。
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random number input stream in a simulation procedure by a low-discrepancy number input stream, variance reductions of several orders have been observed in financial applications. Analysis of stochastic effects in well-mixed chemical reaction networks often relies on sample path simulation using Monte Carlo methods, even though these methods suffer from typical slow convergence rates as a function of the number of sample paths N. This paper investigates the combination of (randomised) quasi-Monte Carlo methods with an efficient sample path simulation procedure, namely -leaping. We show that this combination is often more effective than traditional Monte Carlo simulation in terms of the decay of statistical errors. The observed convergence rate behaviour is, however, non-trivial due to the discrete nature of the models of chemical reactions. We explain how this affects the performance of quasi-Monte Carlo methods by looking at a test problem in standard quadrature.
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影响因子：
4.4
作者：
Gillespie, DT
通讯作者：
Gillespie, DT
影响因子：
4.4
作者：
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Petzold, LR
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作者：
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通讯作者：
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