LINEAR COMPARTMENTAL MODELS: INPUT-OUTPUT EQUATIONS AND OPERATIONS THAT PRESERVE IDENTIFIABILITY
LINEAR COMPARTMENTAL MODELS: INPUT-OUTPUT EQUATIONS AND OPERATIONS THAT PRESERVE IDENTIFIABILITY
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DOI：
10.1137/18m1204826
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发表时间：
2019-01-01
影响因子：
1.9
通讯作者：
Shiu, Anne
中科院分区：
文献类型：
--
作者：
Gross, Elizabeth;Harrington, Heather;Shiu, Anne
本文主要研究数学模型的可辨识性，即参数是否可以从数据中恢复，与其子模型的可辨识性之间的关系。我们特别关注线性房室模型，并研究在添加或删除模型组件后何时保留可识别性。特别是，我们检查是否保留可识别性时，输入，输出，边缘，或泄漏被添加或删除。我们的方法，通过微分代数，是分析特定的输入输出方程的模型和相关的系数映射的雅可比矩阵。我们澄清了这些方程的先验行列式公式，然后用它来证明，在某些假设下，模型的输入输出方程可以理解为某些子模型，我们称之为“输出可达”。“我们的证明使用代数和组合技术。
This work focuses on the question of how identifiability of a mathematical model, that is, whether parameters can be recovered from data, is related to identifiability of its submodels. We look specifically at linear compartmental models and investigate when identifiability is preserved after adding or removing model components. In particular, we examine whether identifiability is preserved when an input, an output, an edge, or a leak is added or deleted. Our approach, via differential algebra, is to analyze specific input-output equations of a model and the Jacobian of the associated coefficient map. We clarify a prior determinantal formula for these equations, and then use it to prove that, under some hypotheses, a model's input-output equations can be understood in terms of certain submodels we call "output-reachable." Our proofs use algebraic and combinatorial techniques.