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 exasperated 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 $\tau$-leap algorithm for simulating well-mixed chemical systems. In particular, the algorithm uses $\tau$-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 leverages the properties of the underlying Poisson formulation, is employed. As illustrated through a number of numerical experiments the hybrid $\tau$ offers significant computational savings when compared to 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.

翻译：我们考虑高效模拟化学动力学随机模型的问题。Gillespie随机模拟算法（SSA）常用于模拟这些模型，但在许多相关场景中，其计算成本迅速变得难以承受。在贝叶斯推断框架下估计化学模型参数时，由于似然函数的难解性需要多次模拟底层系统，这一问题进一步加剧。为解决计算复杂性问题，本文提出一种新颖的混合τ跳跃算法，用于模拟充分混合的化学系统。具体而言，该算法在适用场景（高种群密度）下采用τ跳跃，在必要场景（低种群密度且离散效应不可忽略时）采用SSA，而在中间区域则利用底层泊松公式的性质，结合使用两种方法。通过多项数值实验表明，混合τ跳跃相比SSA能显著降低计算开销，同时不牺牲整体精度。这一特性在贝叶斯推断背景下尤为可贵，因为它允许以较低的计算成本实现随机化学动力学参数的估计。