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：本文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）常用于此类模拟，但在许多实际场景中，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，这一问题更加严峻，因为似然函数的不可解性需要对底层系统进行多次模拟。为解决计算复杂性问题，本文提出了一种新颖的混合τ跳跃算法，用于模拟充分混合的化学反应系统。具体而言，该算法在适用时（高种群密度）采用τ跳跃，在必要时（低种群密度，离散效应不可忽略时）采用SSA。在中间状态区间，则利用底层泊松分布的特性，结合两种方法进行模拟。数值实验表明，与SSA相比，混合τ跳跃算法在不牺牲整体精度的前提下显著降低了计算成本。这一特性在贝叶斯推断背景下尤为有益，使得在降低计算成本的同时实现随机化学动力学的参数估计成为可能。