On validation and invalidation of biological models.
On validation and invalidation of biological models.
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DOI：
10.1186/1471-2105-10-132
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发表时间：
2009-05-07
影响因子：
3
通讯作者：
Papachristodoulou A
中科院分区：
文献类型：
--
作者：
Anderson J;Papachristodoulou A
同一个生物系统常常由几个数学模型来描述，有时甚至是相互竞争的数学模型。这通常会造成混乱周围的有效性，即，哪一个是正确的。然而，这是不必要的，因为模型的有效性无法建立;模型验证实际上是一个用词不当。原则上，关于一个系统模型，人们唯一能做的陈述就是它是不正确的，即无效的，这是一个可以在给定适当的实验数据的情况下建立的事实。由于非线性模型维数高、参数多，无法通过仿真实现失效，因此失效过程往往被忽略或忽略。我们开发了不同的方法来显示如何竞争的常微分方程（ODE）为基础的模型，含有非线性和参数的不确定性，可以使用实验数据无效的相同的生物现象。我们首先强调系统识别和模型失效之间的强烈相互作用，我们描述了一种方法，用于获得候选模型预测和数据之间的误差的下限。然后，我们转向模型失效，并制定了离散时间和连续时间模型失效的方法。该方法是算法和使用半定规划作为计算工具。它强调，试图通过穷举模拟无效的复杂的非线性模型不仅是计算上棘手的，而且是不确定的。从实验数据得出的生物模型永远无法得到验证。事实上，为了理解生物功能，我们应该尝试使与现有数据不相容的模型无效。这项工作描述了一个框架，连续和离散时间的ODE模型的基础上凸优化技术无效。该方法不需要对候选模型进行任何模拟;本文提出的算法具有最坏情况下的多项式时间复杂度，可以为失效问题提供精确的答案。
Very frequently the same biological system is described by several, sometimes competing mathematical models. This usually creates confusion around their validity, ie, which one is correct. However, this is unnecessary since validity of a model cannot be established; model validation is actually a misnomer. In principle the only statement that one can make about a system model is that it is incorrect, ie, invalid, a fact which can be established given appropriate experimental data. Nonlinear models of high dimension and with many parameters are impossible to invalidate through simulation and as such the invalidation process is often overlooked or ignored. We develop different approaches for showing how competing ordinary differential equation (ODE) based models of the same biological phenomenon containing nonlinearities and parametric uncertainty can be invalidated using experimental data. We first emphasize the strong interplay between system identification and model invalidation and we describe a method for obtaining a lower bound on the error between candidate model predictions and data. We then turn to model invalidation and formulate a methodology for discrete-time and continuous-time model invalidation. The methodology is algorithmic and uses Semidefinite Programming as the computational tool. It is emphasized that trying to invalidate complex nonlinear models through exhaustive simulation is not only computationally intractable but also inconclusive. Biological models derived from experimental data can never be validated. In fact, in order to understand biological function one should try to invalidate models that are incompatible with available data. This work describes a framework for invalidating both continuous and discrete-time ODE models based on convex optimization techniques. The methodology does not require any simulation of the candidate models; the algorithms presented in this paper have a worst case polynomial time complexity and can provide an exact answer to the invalidation problem.
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影响因子：
2.7
作者：
Parrilo, PA
通讯作者：
Parrilo, PA
影响因子：
6.8
作者：
Smith, R;Dullerud, GE
通讯作者：
Dullerud, GE
DOI：
10.1007/bf02427917
发表时间：
1997-06-01
期刊：
STOCHASTIC HYDROLOGY AND HYDRAULICS
影响因子：
--
作者：
Beck, MB;Ravetz, JR;Barnwell, TO
通讯作者：
Barnwell, TO
影响因子：
3.4
作者：
Feng, XJ;Rabitz, H
通讯作者：
Rabitz, H
影响因子：
--
作者：
August, Elias;Papachristodoulou, Antonis
通讯作者：
Papachristodoulou, Antonis