Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are modelled using a continuous-time stochastic process, and, depending on the application area of interest, this will typically take the form of a Markov jump process or an It\^o diffusion process. Widespread use of these models is typically precluded by their computational complexity. In particular, performing exact fully Bayesian inference in either modelling framework is challenging due to the intractability of the observed data likelihood, necessitating the use of computationally intensive techniques such as particle Markov chain Monte Carlo (particle MCMC). It is proposed to increase the computational and statistical efficiency of this approach by leveraging the tractability of an inexpensive surrogate derived directly from either the jump or diffusion process. The surrogate is used in three ways: in the design of a gradient-based parameter proposal, to construct an appropriate bridge and in the first stage of a delayed-acceptance step. The resulting approach, which exactly targets the posterior of interest, offers substantial gains in efficiency over a standard particle MCMC implementation.

翻译：随机动力学模型（SKMs）越来越多地被用于解释流行病学、种群生态学和系统生物学等领域中物种相互作用种群所表现出的固有随机性。物种数量使用连续时间随机过程建模，根据所关注的应用领域，这通常采用马尔可夫跳跃过程或Itô扩散过程的形式。这些模型的广泛应用通常受限于其计算复杂性。特别是，由于观测数据似然函数的难处理性，在任一建模框架中执行精确的全贝叶斯推理极具挑战性，因此需使用计算密集型技术，如粒子马尔可夫链蒙特卡洛（粒子MCMC）。本文提出通过利用从跳跃过程或扩散过程中直接推导出的廉价替代模型的易处理性，来提高该方法的计算和统计效率。该替代模型以三种方式使用：设计基于梯度的参数提议、构建适当的桥接步骤，以及延迟接受阶段的第一步。所提出的方法能够精确地针对后验分布，相较于标准粒子MCMC实现，在效率上实现了显著提升。