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：基于似然函数的推断在随机非线性动力系统中（如化学反应网络和生物钟系统）本质上非常复杂，且大多局限于规模较小且过度简化的理想系统。近期在解析可处理的近似条件概率分布方面取得的进展，使长期动力学能够被精确建模，并使精确贝叶斯推断所需的大量模型评估变得可行。我们提出了一种针对具有振荡行为的随机非线性动力系统的推断新方法，并证明这些模型中的参数可以通过模拟数据进行合理估计。基于模型费希尔信息矩阵的初步分析可指导贝叶斯推断的实施。研究表明，这种参数灵敏度分析能够预测哪些参数在实际中是可识别的。我们比较了多种马尔可夫链蒙特卡洛算法，结果显示并行回火算法对这些系统（常表现出多模态后验分布）始终是最优方法。