Ramkrishna Doraiswami, Shu Che-Chi, Tran Vu
School of Chemical Engineering, Purdue University , West Lafayette, Indiana 47907, United States.
Ind Eng Chem Res. 2014 Dec 10;53(49):18975-18981. doi: 10.1021/ie502929q. Epub 2014 Sep 22.
The "Tau-Leap" strategy for stochastic simulations of chemical reaction systems due to Gillespie and co-workers has had considerable impact on various applications. This strategy is reexamined with Chebyshev's inequality for random variables as it provides a rigorous probabilistic basis for a measured τ-leap thus adding significantly to simulation efficiency. It is also shown that existing strategies for simulation times have no probabilistic assurance that they satisfy the τ-leap criterion while the use of Chebyshev's inequality leads to a specified degree of certainty with which the τ-leap criterion is satisfied. This reduces the loss of sample paths which do not comply with the τ-leap criterion. The performance of the present algorithm is assessed, with respect to one discussed by Cao et al. (, , 044109), a second pertaining to binomial leap (Tian and Burrage , , 10356; Chatterjee et al. , , 024112; Peng et al. , , 224109), and a third regarding the midpoint Poisson leap (Peng et al., 2007; Gillespie , , 1716). The performance assessment is made by estimating the error in the histogram measured against that obtained with the so-called stochastic simulation algorithm. It is shown that the current algorithm displays notably less histogram error than its predecessor for a fixed computation time and, conversely, less computation time for a fixed accuracy. This computational advantage is an asset in repetitive calculations essential for modeling stochastic systems. The importance of stochastic simulations is derived from diverse areas of application in physical and biological sciences, process systems, and economics, etc. Computational improvements such as those reported herein are therefore of considerable significance.
由吉莱斯皮及其同事提出的用于化学反应系统随机模拟的“τ跳跃”策略，已在各种应用中产生了重大影响。本文利用随机变量的切比雪夫不等式对该策略进行了重新审视，因为它为测量的τ跳跃提供了严格的概率基础，从而显著提高了模拟效率。研究还表明，现有的模拟时间策略没有概率保证它们满足τ跳跃准则，而使用切比雪夫不等式可得出满足τ跳跃准则的特定确定度。这减少了不符合τ跳跃准则的样本路径的损失。相对于曹等人（……，044109）讨论的一种算法、与二项式跳跃相关的第二种算法（田和伯拉奇……，10356；查特吉等人……，024112；彭等人……，224109）以及关于中点泊松跳跃的第三种算法（彭等人，2007；吉莱斯皮……，1716），对本算法的性能进行了评估。通过估计与所谓的随机模拟算法所得直方图相比测量直方图中的误差来进行性能评估。结果表明，在固定计算时间下，当前算法显示出的直方图误差明显小于其前身，反之，在固定精度下，计算时间更短。这种计算优势对于随机系统建模必不可少的重复计算来说是一项资产。随机模拟的重要性源于物理和生物科学、过程系统以及经济学等不同应用领域。因此，本文所报道的此类计算改进具有相当重要的意义。
