Optimization experiments, design

To design an experiment means to choose the optimal experiment design to be used simultaneously for varying all the analyzed factors. By designing an experiment one gets more precise data and more complete information on a studied phenomenon with a minimal number of experiments and the lowest possible material costs. The development of statistical methods for data analysis, combined with development of computers, has revolutionized the research and development work in all domains of human activities. 

A standard E-optimal experiment design was compared with the newly introduced OMBRE strategy at a variable number of updates of design variables. The following assumptions are made ... 

Figure 1 Global precision Q.0 (a) and GTF (b) for selected re-design configurations at a variable number of updates n p = 0 stands for a standard E-optimal experiment design).

Chapter 9 shows how compartmental models may be used to describe physiological systems, for example, pharmacokinetics. The production, distribution, transport, and interaction of exogenous materials, such as drugs or tracers, and endogenous materials, such as hormones, are described. Examples of both linear and nonlinear compartmental models are presented, as well as parameter estimation, optimal experiment design, and model validation. 

At this point one has a compartmental model structure, a description of the measurement error, and a numerical value of the parameters together with the precision with which they can be estimated. It is now appropriate to address the optimal experiment design issue. The rationale of optimal experiment design is to act on design variables such as number of test input and outputs, form of test inputs, number of samples and sampling schedule, and measurement errors so as to maximize, according to some criterion, the precision with which the compartmental model parameters can be estimated [DiStefano, 1981 Carson et al, 1983 Landaw and DiStefano, 1984 Walter and Pronzato, 1990]. 

In a Bayes estimation context, optimal experiment design is a more difficult task (see [Walter and Pronzato, 1990] for a survey). Applications have thus been less than those with a Fisher approach, also because the numerical implementation of the theoretical results is much more demanding. 

Finally, some results on optimal experiment design in a population parameter estimation context have also been recently presented [Hooker et al., 2003]. 

In order to design the response surface optintization experiment and determine the influence of every factor, the first task is to confirm the optimum influence range of every factor on experimental results, to guarantee the feasibility of the response surface optimization experiment design. The single factor sample production parameters are showed in Table I. 

A Priori Identifiability Parameter Estimation Optimal Experiment Design Validation References... 

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