Sandmann Werner
Clausthal University of Technology, Department of Mathematics, Clausthal-Zellerfeld, Germany.
Math Biosci. 2009 Sep;221(1):43-53. doi: 10.1016/j.mbs.2009.06.006. Epub 2009 Jul 2.
Stochastic simulation of biological systems proceeds by repeatedly generating sample paths or trajectories of the underlying stochastic process, from which many relevant and important system properties can be obtained. While a great deal of research is targeted towards accelerated trajectory generation, issues concerned with the variability across trajectories are often neglected. Advanced methods for properly quantifying the statistical accuracy and determining a reasonable number of trajectories are hardly addressed formally in the context of biological system simulation, though mathematical statistics provides a large body of powerful theory. We invoke this theory and show how mathematically well-founded sequential estimation approaches serve for systematically generating enough but not too many trajectories for achieving a certain prescribed accuracy. The practical applicability is demonstrated and illustrated by numerical examples through simulation studies of an immigration-death process and a gene regulatory network.
生物系统的随机模拟是通过反复生成基础随机过程的样本路径或轨迹来进行的，从中可以获得许多相关且重要的系统属性。虽然大量研究致力于加速轨迹生成，但与轨迹间变异性相关的问题却常常被忽视。尽管数理统计学提供了大量强大的理论，但在生物系统模拟的背景下，很少正式探讨用于正确量化统计精度和确定合理轨迹数量的先进方法。我们运用这一理论，并展示了数学基础良好的序贯估计方法如何用于系统地生成足够但又不过多的轨迹，以实现特定的规定精度。通过对一个迁入 - 死亡过程和一个基因调控网络的模拟研究，用数值示例证明并说明了该方法的实际适用性。
