Statistical methods in model discrimination

Abstract

Particularly in the chemical kinetic field but also in others in chemistry and engineering there has been much recent attention on the use of statistics in discriminating between rival models. There are two related basic problems. The first is to design experiments which will be most informative in determining which of several possible mathematical models is the “correct” one. Simple illustrations are given of the solution of this problem by different methods, such as the criteria of Roth, Box and Hill and of others, including some work done by R. S. Hawkins and the author on expected entropy change. The second problem is to analyze the data when received. A sampling of likelihood and Bayesian approaches to this problem is described with examples.

Discrimination and goodness of fit of multiresponse mechanistic models

“…The factor 2-'". in thcsc formulas removes the tendency toward overfitting noted hy Reilly (1970) and Chow (1981) for discrimination methods based on maximized likelihood.…”

Model selection: An overview of practices in chemical engineering

“…Ideally, in the first case discrimination measures should be based on the simple L a norm, such as in eq. (10). In the latter case, the full eqs.…”

“…Finally, this summary ends with the entropy measure, which goes back to the work of Reilly [10]. Entropy is defined as − m p(m|n, I) ln(p(m|n, I) and this should be reduced with each subsequent experiment.…”

Choosing the right model: Case studies on the use of statistical modeldiscrimination experiments

“…As in the other examples, a few parameter estimation experiments were always simulated first in order to ensure (Reilly, 1970) C. Hsiang and Reilly (1971) Implicit penultimate …”

“…However, they have not been extensively evaluated or systematically examined for their sensitivity to factors such as experimental error level or the quality of initial parameter estimates. For this reason, three of the most promising model discrimination methods were chosen for extensive comparison.The methods chosen were the Buzzi-Ferraris and Forzatti method (Buzzi-Ferraris and Forzatti, 1983;Buzzi-Ferraris et al, 1984, 1990, the exact entropy method (Reilly, 1970), and the Hsiang and Reilly (1971) method. These three ?Present address: Novacor Research and Technology Corporation, 2928-*Author to whom correspondence should be addressed.…”