Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

中文翻译：

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系统生物学中随机微分方程模型的可辨识性分析


数学模型通常根据实验数据进行校准，目标范围从建立预测模型到量化无法测量的参数。是否可以从现有数据中获得可靠的参数估计很容易被忽视。此类参数可识别性问题对于模型的预测能力和可以获得的机制洞察力都有重要影响。可识别性分析对于确定性常微分方程 (ODE) 模型来说已经很成熟，但在随机模型中没有普遍采用的方法来分析可识别性。我们提供了可识别性分析的简单介绍，并通​​过四个实际案例研究展示了如何将 ODE 模型分析的现有思想应用于随机微分方程 (SDE) 模型。为了评估结构可识别性，我们使用开源软件工具研究了描述随机过程统计矩的常微分方程。使用实用的合成数据和马尔可夫链蒙特卡罗方法，我们在可用数据的背景下评估参数的可识别性。我们的分析表明，SDE 模型通常可以提取比确定性描述更多的参数信息。用于执行分析的所有代码都可以在 Github 上找到。