Optimization and interpretation of results

The classical approach to parameter estimation, optimization of the objective function, encompasses all the experimental observations of the study. The procedures involved have been outlined earlier. Here we are more concerned with the interpretation of results, a subject that causes quite a lot of confusion. 

To test the adequacy of a model one needs to determine independently an estimate of the error variance free of systematic errors. The obvious source of systematic errors is the incomplete knowledge of relationships (7.1). Determination of these instrumental functions, assessed by so-called calibrating experiments, constitutes modeling of the instrumental process, but the adequacy of the model [Eq. (7.1)] cannot be easily established, if at all. Let us 

Considering this, it is more appropriate to compare confidence regions, bearing in mind the following possible situations (Fig. 6)  

Optimization of the overall objective function places a tremendous demand for computer time. Every iteration requires integration of Eqs. (2.2) for all experimental runs and the number of iterations must be substantial since at least two parameters must be estimated for each reaction considered. Box and Hunter (1962) proposed a simpler method, suitable when experiments are carried out at various exactly known temperatures, each isothermally 

Even though the computed responses were close to the experimentally observed ignition delays, 9 was not of interest for the reason of unknown gasdynamics. 

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Stochastic outcomes complicate feedback to optimization and interpretation of results. 

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