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:在化学反应网络和生物时钟系统中发现的非线性动态系统中,基于可能性的推论,如化学反应网络和生物时钟系统中发现的推论,具有内在的复杂性,主要限于小的和不现实的简单系统。最近在分析上对基本有条件概率分布的可移植近似值方面的最新进展,使得能够准确地模拟长期动态,并使精确的贝叶斯推论所需的大量模型评估更加可行。我们提出了一种新的方法,用以推断显示显示非线性动态系统的振荡行为,并表明这些模型中的参数可以从模拟数据中现实地估算。基于该模型的渔业信息矩阵的初步分析可以指导Bayesian推论的实施。我们表明,这种参数敏感度分析可以预测哪些参数实际上可以确定。一些Markov连锁的蒙特卡洛算法进行了比较,我们的结果表明,平行的调控算法始终是这些系统的最佳方法,这些系统经常展示多模式的后传波分布。