Determining the parametric structure of models
Determining the parametric structure of models
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DOI：
10.1016/j.mbs.2010.08.004
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发表时间：
2010-11-01
影响因子：
4.3
通讯作者：
Titterington, D. M.
中科院分区：
文献类型：
--
作者：
Cole, D. J.;Morgan, B. J. T.;Titterington, D. M.
在本文中，我们发展了一种确定模型参数结构的综合方法。这涉及到考虑模型是否具有参数冗余性和研究模型的可辨识性。所采用的方法利用了详尽的总结，即唯一定义模型的数量。我们回顾和推广了以前关于计算适当导数矩阵的符号秩来检测参数冗余的工作，然后基于矩阵分解开发了进一步的工具用于该框架内。在复杂模型中，符号等级很难计算，可以使用重新参数化和找到简化形式的详尽摘要在结构上进行简化。以生态学、隔室模型和贝叶斯网络为例，说明了本文的方法。随着生物科学和其他领域的模型变得越来越复杂，这项工作成为热门话题。(C)2010 Elsevier Inc.保留所有权利。
In this paper we develop a comprehensive approach to determining the parametric structure of models. This involves considering whether a model is parameter redundant or not and investigating model identifiability. The approach adopted makes use of exhaustive summaries, quantities that uniquely define the model. We review and generalise previous work on evaluating the symbolic rank of an appropriate derivative matrix to detect parameter redundancy, and then develop further tools for use within this framework, based on a matrix decomposition. Complex models, where the symbolic rank is difficult to calculate, may be simplified structurally using reparameterisation and by finding a reduced-form exhaustive summary. The approach of the paper is illustrated using examples from ecology, compartment modelling and Bayes networks. This work is topical as models in the biosciences and elsewhere are becoming increasingly complex. (C) 2010 Elsevier Inc. All rights reserved.