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：我们研究了化学动力学随机模型的高效模拟问题。Gillespie随机模拟算法（SSA）常被用于模拟此类模型，但在许多实际应用场景中，其计算成本会迅速达到难以承受的程度。在贝叶斯推断背景下估计化学模型参数时，由于似然函数的难以处理性需要对底层系统进行多次模拟，这一问题变得尤为突出。为应对计算复杂性问题，本文提出了一种用于模拟充分混合化学体系的新型混合τ-跳跃算法。该算法的核心在于：在适宜场景（高种群密度）采用τ-跳跃方法，在必要场景（低种群密度，离散效应不可忽略时）采用SSA方法。在中间状态区域，则结合两种方法并充分利用底层泊松公式的特性。通过大量数值实验证明，与SSA相比，混合τ-跳跃算法在保持整体精度的同时能显著节省计算资源。这一特性在贝叶斯推断背景下尤其重要，使得以更低计算成本实现随机化学动力学参数估计成为可能。