Discriminant analysis error rate

Fig. 9-9 demonstrates the results of MVDA for the three investigated territories in the plane of the computed two discriminant functions. The separation line corresponds to the limits of discrimination for the highest probability. The results prove that good separation of the three territories with a similar geological background is possible by means of discriminant analysis. The misclassification rate amounts to 13.0%. The scattering radii of the 5% risk of error of the multivariate analysis of variance overlap considerably. They demonstrate also that the differences in the multivariate data structure of the three territories are only small. 

D. Hirst, Error-rate Estimation in Multiple-Group Linear Discriminant Analysis, Technometrics, 38 (1996), 389-399. 

Kolata, G. (2002). Breast cancer Genes are tied to death rates. New York Times, December 19. Lachenbruch, P. A., and Mickey, M. R. (1968). Estimation of error rates in discriminant analysis. Technometrics, 10 1-11. 

Regression analysis is often employed to fit experimental data to a mathematical model. The purpose may be to determine physical properties or constants (e.g., rate constants, transport coefficients), to discriminate between proposed models, to interpolate or extrapolate data, etc. The model should provide estimates of the uncertainty in calculations from the resulting model and, if possible, make use of available error in the data. An initial model (or models) may be empirical, but with advanced knowledge of reactors, distillation columns, other separation devices, heat exchangers, etc., more sophisticated and fundamental models can be employed. As a starting point, a linear equation with a single independent variable may be initially chosen. Of importance, is the mathematical model linear In general, a function,/, of a set of adjustable parameters, 3y, is linear if a derivative of that function with respect to any adjustable parameter is not itself a function of any other adjustable parameter, that is. 

In this paper I have attempted to demonstrate a method for the development of hyperbolic rate models that are adequate for the design of chemical reactors. The method is rapid and overcomes most of the problems that historically have hampered the development of such models for complex reactions. I have shown that the quality of fit of a model to error-containing data is a poor criterion for model discrimination, and that several models may predict almost equally well. This, of course, has been known for a long time, but it has not been widely recognized that the model that fits the data least well may be the best model, and that the converse also may be true. In the final analysis... 

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