Here we present the sum of squares formalism which is used to relax and solve the optimization problems posed by the various approaches for model discrimination considered in this paper.
In this framework, model discrimination is based on a Bayesian approach, which assigns prior 'goodness' probabilities to each model, updates these after each experiment and chooses the model with the likelihood that has become sufficiently large compared to others.
Application of the MFP approach resulted in improved model discrimination (c statistic = 0.843 versus 0.835 for the standard model), as well as excellent fit (Hosmer Lemeshow P = 0.71).
In this paper, the performance of this approach is evaluated by comparing it with the performance of other, established approaches to optimal experimental design for model discrimination.
Kreutz and Timmer [ 19] gave a review of approaches to parameter estimation and model discrimination (discussing the Akaike Information Criterion, the likelihood ratio test, and alternative forms of the sum of squared differences between two models' outputs).
In the first approach, the Initial condition design for model discrimination, we find the initial state of the system which results in the most discriminating output between the two examined models [ 23].
An exploration of time-dependent modeling techniques, a more elaborate variable selection procedure, a more sophisticated multiclass discrimination approach, and the incorporation of other types of sensors in our measuring devices for added redundancy, are also envisioned.
Chen and Asprey [ 17] developed statistical approaches to parameter estimation, the assessment of model fit, and model discrimination, assuming that the response variables are uncertain.
Here we compare this method to the nonlinear Sigma-Point approach for a nonlinear, multi-stable model and show its advantage for model discrimination, especially for large parameter variances.
We demonstrated our approach with two examples of biochemical processes, showing that it can perform model discrimination and provide good parameter estimates, even if only incomplete and uncertain measurements are available.
