Trigo Trindade Thomas, Zygalakis Konstantinos C
Mathematics, EPFL, Lausanne, Switzerland.
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, UK.
R Soc Open Sci. 2024 Dec 4;11(12):240157. doi: 10.1098/rsos.240157. eCollection 2024 Dec.
We consider the problem of efficiently simulating stochastic models of chemical kinetics. The Gillespie stochastic simulation algorithm (SSA) is often used to simulate these models; however, in many scenarios of interest, the computational cost quickly becomes prohibitive. This is further exacerbated in the Bayesian inference context when estimating parameters of chemical models, as the intractability of the likelihood requires multiple simulations of the underlying system. To deal with issues of computational complexity in this paper, we propose a novel hybrid τ-leap algorithm for simulating well-mixed chemical systems. In particular, the algorithm uses τ-leap when appropriate (high population densities), and SSA when necessary (low population densities, when discrete effects become non-negligible). In the intermediate regime, a combination of the two methods, which uses the properties of the underlying Poisson formulation, is employed. As illustrated through a number of numerical experiments, the hybrid τ offers significant computational savings when compared with SSA without, however, sacrificing the overall accuracy. This feature is particularly welcomed in the Bayesian inference context, as it allows for parameter estimation of stochastic chemical kinetics at reduced computational cost.
我们考虑有效模拟化学动力学随机模型的问题。吉莱斯皮随机模拟算法（SSA）常被用于模拟这些模型；然而，在许多感兴趣的场景中，计算成本很快就会变得过高。在贝叶斯推断的背景下估计化学模型参数时，这种情况会进一步恶化，因为似然性的难处理性需要对基础系统进行多次模拟。为了处理本文中的计算复杂性问题，我们提出了一种用于模拟充分混合化学系统的新型混合τ跳跃算法。具体而言，该算法在适当的时候（高种群密度）使用τ跳跃，在必要的时候（低种群密度，当离散效应变得不可忽略时）使用SSA。在中间区域，采用结合了两种方法的组合，该组合利用了基础泊松公式的性质。正如通过一些数值实验所表明的那样，与SSA相比，混合τ算法在不牺牲整体准确性的情况下显著节省了计算量。在贝叶斯推断的背景下，这一特性尤其受欢迎，因为它允许以降低的计算成本对随机化学动力学进行参数估计。
