Optimal Sequential Discrimination

The criterion is easily extended to more than two models, as follows  

is the pooled estimate of variance plus lack of fit (D.F.X is the degrees of freedom associated with the ith estimate of error variance plus lack of fit, and m is the number of rival models. 

Whenever Xt exceeds the tabulated value the model corresponding to the largest estimate of error variance is discarded and Xc is recalculated. Another 

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Finally, we should remark that sequential methods for the optimal discrimination of models and the optimal estimation of parameters are discussed in refs. 25 and 32, for example. 

Sequential Design for Optimal Discrimination between Rival... 

When the models are nonlinear in the parameters, Xis replaced by J. An example of application of sequential design for optimal estimation is given by Van Parijs et al. [1986] in their study of benzothiophene hydrogenolysis. At 533 K the desired accuracy of the parameters of the equations given in Example 2.6.4.A was reached after four more experiments beyond the seven required for discriminating between the 16 rival models. In total, no more than 16 experiments were required for the four temperature levels that were investigated. 

The steps involved in sequential experimental design for optimal discrimination and estimation can be represented in a simplified flow diagram as shown in Fig. 2.8-1. The loops can even be closed so that the settings of the independent variables are implemented on the experimental setup directly by the computer. 

J. Handler, R. Lavie and H. Sheintuch An automated catalytic system for the sequential optimal discrimination between rival models, Chem.Eng.Sci. (1983)979-990 /25/ L.H. Rose, C. Schifferli and D.W.T. Rippin Computer application in the analysis of chemical data and plants, Proc.Chemda-ta Helsinki ( 1977)132-136... 

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