Generalized sensitivities and optimal experimental design
Generalized sensitivities and optimal experimental design
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DOI：
10.1515/jiip.2010.002
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发表时间：
2010-04-01
影响因子：
1.1
通讯作者：
Kappel, Franz
中科院分区：
文献类型：
--
作者：
Banks, H. T.;Dediu, Sava;Kappel, Franz
通过引入一个抽象的框架，考虑对给定的数据y，利用加权最小二乘准则J（d）（y，theta）= Sigma（n）（i=1）1/sigma（t（i））（2）（y（t（i））-f（t（i），theta））（2）估计建模参数theta的问题.我们采取最佳设计的观点，一般前提（通过示例说明）是，在收集的任何数据中，关于估计θ的信息内容可能从一个时间测量到另一个时间测量有很大变化，并且在这方面，一些测量可能比其他测量提供更多的信息。我们提出了数学工具，其可以用于以几乎最佳的方式收集数据，通过指定要进行的测量中的时间采样的持续时间和分布，从而提高准确度（即，我们回顾了传统的和广义的灵敏度函数的概念，并使用这些来开发一种策略，以确定“最佳”的最终时间T的实验，这是基于时间演化的灵敏度函数和条件数的Fisher信息矩阵。我们说明的作用的灵敏度函数作为工具，在最优设计的实验，特别是在寻找“最佳”的抽样分布。整个数值例子来激励和说明的想法。
We consider the problem of estimating amodeling parameter theta using a weighted least squares criterion J(d) (y, theta) = Sigma(n)(i=1) 1/sigma(t(i))(2)(y(t(i))-f(t(i), theta))(2) for given data y by introducing an abstract framework involving generalized measurement procedures characterized by probability measures. We take an optimal design perspective, the general premise (illustrated via examples) being that in any data collected, the information content with respect to estimating theta may vary considerably from one time measurement to another, and in this regard some measurements may be much more informative than others. We propose mathematical tools which can be used to collect data in an almost optimal way, by specifying the duration and distribution of time sampling in the measurements to be taken, consequently improving the accuracy (i.e., reducing the uncertainty in estimates) of the parameters to be estimated.We recall the concepts of traditional and generalized sensitivity functions and use these to develop a strategy to determine the "optimal" final time T for an experiment; this is based on the time evolution of the sensitivity functions and of the condition number of the Fisher information matrix. We illustrate the role of the sensitivity functions as tools in optimal design of experiments, in particular in finding "best" sampling distributions. Numerical examples are presented throughout to motivate and illustrate the ideas.