Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple systems. Recent advances in analytically tractable approximations to the underlying conditional probability distributions enable long-term dynamics to be accurately modelled, and make the large number of model evaluations required for exact Bayesian inference much more feasible. We propose a new methodology for inference in stochastic non-linear dynamical systems exhibiting oscillatory behaviour and show the parameters in these models can be realistically estimated from simulated data. Preliminary analyses based on the Fisher Information Matrix of the model can guide the implementation of Bayesian inference. We show that this parameter sensitivity analysis can predict which parameters are practically identifiable. Several Markov chain Monte Carlo algorithms are compared, with our results suggesting a parallel tempering algorithm consistently gives the best approach for these systems, which are shown to frequently exhibit multi-modal posterior distributions.

翻译：在随机非线性动力系统（如化学反应网络和生物钟系统）中进行基于似然性的推断具有固有的复杂性，且主要局限于小型且不切实际的简单系统。近期在基础条件概率分布解析可处理近似方法上的进展，使得长期动力学能够被精确建模，并大幅提升了精确贝叶斯推断所需的大量模型评估的可行性。我们提出了一种新的方法，用于在表现出振荡行为的随机非线性动力系统中进行推断，并展示了这些模型中的参数可以从模拟数据中得到实际估计。基于模型费舍尔信息矩阵的初步分析可以指导贝叶斯推断的实施。我们证明，这种参数敏感性分析可以预测哪些参数是实际可识别的。我们比较了几种马尔可夫链蒙特卡洛算法，结果表明，对于这些常表现出多峰后验分布的系统，并行回火算法始终能提供最佳方法。