Discrimination procedures generalization

Holter SM, Danysz W, Spanagel R (2000) Novel uncompetitive N-methyl-D-aspartate (NMDA)-receptor antagonist MRZ 2/579 suppresses ethanol intake in long-term ethanol-experienced rats and generalizes to ethanol cue in drug discrimination procedure. J Pharmacol Exp Ther 292 545-552... 

A systanatic general procedure for selecting suitable structural models, even in multiphase systans, has been proposed in Ref. [113]. This method is based on a model discrimination procedure. If a component has unknown thermal conductivity, the method estimates the dependence of the temperature on the unknown thermal conductivity, and the suitable structural models simultaneously. 

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

To judge the performance of the discriminant functions and the classification procedure in respect of future samples one can calculate misclassification probabilities or error rates. But these probabilities cannot be calculated in general because they depend on the unknown density functions of the classes. Instead we can usually utilize a measure called apparent error rate. The value of this quantity is easily calculated from the classification or confusion matrix based on the samples of the training set. For example with two classes we can have the following matrix ... 

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