标题： 基于似然的可观测性分析和动态模型预测的置信区间 显示英文标题

标题： Likelihood based observability analysis and confidence intervals for predictions of dynamic models

摘要： 生化网络的机制动态模型，如常微分方程（ODEs），包含未知参数，如反应速率常数和化合物的初始浓度。参数数量众多以及它们对模型响应的非线性影响阻碍了参数估计置信区域的确定。同时，将参数不确定性转化为模型预测置信区间的经典方法几乎不可行。在本文中表明，即使参数估计置信区域的形状任意复杂且高维，所谓的预测轮廓似然仍能产生可靠的模型预测置信区间。动态状态的预测置信区间允许基于数据的可观测性分析。该方法将高维参数空间采样问题转化为一维预测空间的评估。如果存在不可识别参数，导致某些未充分指定的模型预测，可以将其解释为不可观测性，该方法同样适用。此外，引入了一种验证轮廓似然，当需要解释噪声验证实验时应使用该方法。通过两个例子展示了预测和验证轮廓似然方法的特性和适用性，一个是对两个连续反应进行描述的小而具有指导意义的ODE模型，另一个是针对MAP激酶信号转导通路的真实ODE模型。所提出的通用方法构成了一种可观测性分析概念，并用于生成模型预测的可靠置信区间，不仅适用于，而且特别适用于生物系统的数学模型。 显示英文摘要

摘要： Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as well as their nonlinear impact on the model responses hamper the determination of confidence regions for parameter estimates. At the same time, classical approaches translating the uncertainty of the parameters into confidence intervals for model predictions are hardly feasible. In this article it is shown that a so-called prediction profile likelihood yields reliable confidence intervals for model predictions, despite arbitrarily complex and high-dimensional shapes of the confidence regions for the estimated parameters. Prediction confidence intervals of the dynamic states allow a data-based observability analysis. The approach renders the issue of sampling a high-dimensional parameter space into evaluating one-dimensional prediction spaces. The method is also applicable if there are non-identifiable parameters yielding to some insufficiently specified model predictions that can be interpreted as non-observability. Moreover, a validation profile likelihood is introduced that should be applied when noisy validation experiments are to be interpreted. The properties and applicability of the prediction and validation profile likelihood approaches are demonstrated by two examples, a small and instructive ODE model describing two consecutive reactions, and a realistic ODE model for the MAP kinase signal transduction pathway. The presented general approach constitutes a concept for observability analysis and for generating reliable confidence intervals of model predictions, not only, but especially suitable for mathematical models of biological systems.