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Optimal experimental design for linear time invariant state–space models
Statistics and Computing ( IF 2.2 ) Pub Date : 2021-05-28 , DOI: 10.1007/s11222-021-10020-y
Belmiro P. M. Duarte , Anthony C. Atkinson , Nuno M. C. Oliveira

The linear time invariant state–space model representation is common to systems from several areas ranging from engineering to biochemistry. We address the problem of systematic optimal experimental design for this class of model. We consider two distinct scenarios: (i) steady-state model representations and (ii) dynamic models described by discrete-time representations. We use our approach to construct locally D-optimal designs by incorporating the calculation of the determinant of the Fisher Information Matrix and the parametric sensitivity computation in a Nonlinear Programming formulation. A global optimization solver handles the resulting numerical problem. The Fisher Information Matrix at convergence is used to determine model identifiability. We apply the methodology proposed to find approximate and exact optimal experimental designs for static and dynamic experiments for models representing a biochemical reaction network where the experimental purpose is to estimate kinetic constants.



中文翻译:

线性时不变状态空间模型的优化实验设计

线性时不变状态-空间模型表示对于从工程到生物化学的多个领域的系统来说是常见的。我们针对此类模型解决了系统优化实验设计的问题。我们考虑两种不同的场景:(i)稳态模型表示和(ii)由离散时间表示描述的动态模型。我们使用我们的方法通过在非线性规划公式中结合 Fisher 信息矩阵的行列式计算和参数灵敏度计算来构建局部 D 最优设计。全局优化求解器处理由此产生的数值问题。收敛时的 Fisher 信息矩阵用于确定模型的可识别性。

更新日期:2021-05-30
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