Identifiability of linear compartmental tree models and a general formula for input-output equations
Identifiability of linear compartmental tree models and a general formula for input-output equations
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DOI：
10.1016/j.aam.2023.102490
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发表时间：
2023-02-03
影响因子：
1.1
通讯作者：
Sullivant，Seth
中科院分区：
文献类型：
--
作者：
Bortner，Cashous;Gross，Elizabeth;Sullivant，Seth
线性隔室模型理论中的一个基本问题是如何直接从模型的组合中评估模型是否具有结构可识别性，即参数值是否可以从无噪声数据中推断出来。我们的主要结果完全回答了这个问题的模型（有一个输入和一个输出），其中底层图是一个双向树；此外，这些模型的可识别性可以通过视觉验证。这种结构的模型包括两类经常出现在生物学应用中的模型：链链模型和乳状模型。我们对这些模型的分析得到了两个支持结果的支持，这两个结果本身就很重要。一个结果给出了输入-输出方程（某些可用于确定可识别性的方程）系数的第一个通用公式，该公式允许输入和输出处于不同的隔间中。在另一个支持结果中，我们证明了当模型以特定的方式扩大和改变时，包括在现有的隔室中添加一个具有双向边的新隔室，可识别性是保留的。
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable – that is, whether parameter values can be inferred from noiseless data – directly from the combinatorics of the model. Our main result completely answers this question for models (with one input and one output) in which the underlying graph is a bidirectional tree; moreover, identifiability of such models can be verified visually. Models of this structure include two families of models often appearing in biological applications: catenary and mammillary models. Our analysis of such models is enabled by two supporting results, which are significant in their own right. One result gives the first general formula for the coefficients of input-output equations (certain equations that can be used to determine identifiability) that allows for input and output to be in distinct compartments. In another supporting result, we prove that identifiability is preserved when a model is enlarged and altered in specific ways involving adding a new compartment with a bidirected edge to an existing compartment.