UCLA, Department of Mathematics, USA.
Math Biosci. 2011 Sep;233(1):19-31. doi: 10.1016/j.mbs.2011.06.001. Epub 2011 Jul 18.
When examining the structural identifiability properties of dynamic system models, some parameters can take on an infinite number of values and yet yield identical input-output data. These parameters and the model are then said to be unidentifiable. Finding identifiable combinations of parameters with which to reparameterize the model provides a means for quantitatively analyzing the model and computing solutions in terms of the combinations. In this paper, we revisit and explore the properties of an algorithm for finding identifiable parameter combinations using Gröbner Bases and prove useful theoretical properties of these parameter combinations. We prove a set of M algebraically independent identifiable parameter combinations can be found using this algorithm and that there exists a unique rational reparameterization of the input-output equations over these parameter combinations. We also demonstrate application of the procedure to a nonlinear biomodel.
在检查动态系统模型的结构可识别性属性时，有些参数可以取无数个值，但仍能产生相同的输入-输出数据。这些参数和模型被称为不可识别的。找到可识别的参数组合，用这些参数组合重新参数化模型，提供了一种定量分析模型并根据这些组合计算解的方法。在本文中，我们重新审视并探索了使用 Gröbner 基寻找可识别参数组合的算法的性质，并证明了这些参数组合的有用理论性质。我们证明了可以使用该算法找到一组代数独立的可识别参数组合，并且在这些参数组合上存在输入-输出方程的唯一有理参数化。我们还展示了该过程在非线性生物模型中的应用。
