Cross-validated error rate

In order to characterise wine samples into the mentioned four classes, a supervised pattern recognition method (LDA) was applied. The results obtained gave 100% correct classification for the three classes (Barbera Oltrepo, Barbera Piemonte and Barbera Alba) and only one Barbera Asti sample was not correctly classified (cross-validation error rate 1.89%). 

Efron, B. J. Am. Stat. Assoc. 78, 1983, 316-331. Estimating the error rate of a prediction rule Improvement on cross-validation. 

Simon et al. (14) also showed that cross-validating the prediction rule after selection of differentially expressed genes from the full data set does little to correct the bias of the re-substitution estimator 90.2% of simulated data sets with no true relationship between expression data and class still result in zero misclassifications. When feature selection was also re-done in each cross-validated training set, however, appropriate estimates of mis-classification error were obtained the median estimated misclassification rate was approximately 50%. 

For a more realistic estimate of the future error one splits the total data set into a training and a prediction part. With the training set the discriminant functions are calculated and with the objects of the prediction or validation set, the error rate is then calculated. If one has insufficient samples for this splitting, other methods of cross-validation are useful, especially the holdout method of LACHENBRUCH [1975] which is also called jackknifing or leaving one out . The last name explains the procedure For every class of objects the discriminant function is developed using all the class mem-... 

Efron, B. (1983). Estimating the Error Rate of a Prediction Rule Improvement on Cross-Validation. Journal of American Statistical Association, 78, 316-331. 

Take mean of error. rate which contains v error rates from cross-validation SET i element of resamp. error to average of error, rate... 

The result of data processing for the data set in Table 1.3 is quite similar. Although the rate of correctness in training process increases very quickly (it means that the structure of the data set is relatively simple and can be imitated by using ANN very easily), the minimum number of errors in prediction test (by LOO cross-validation method) of ANN is still higher than that of support vector machine, as shown in Fig. 1.4. 

By SVC with linear kernel, the classification of class 1 and 2 is rather good, and the rate of correctness of prediction is 91% in LOO cross-validation. The relative averaged absolute error of the prediction of AF by SVR in LOO cross-validation is lower than 10%. 

Observed agreement between the experimental and model cross-relaxation rates within the estimated error limits confirms validity of the full matrix analysis procedure but not necessarily its usefulness. Namely, the agreement is achieved mainly within the broad limits of cross-relaxation rate errors. Errors span the range 0.25 to 0.62 s but are clustered around the values 0.35 s and 0.55 s All the errors involving cross-relaxation rates of ProH and GlyH are clustered around 0.35 s . This is mainly because... 

The presentation of data is a critical part of any beam experiment. On more than one occasion, misleading inferences have been drawn from data which were quite valid in their raw state, but which had been inadequately transformed into a form suitable for interpretation. Such errors are often more subtle and harder to detect than those due to failures in laboratory technique. In classical experiments, a rate constant or a cross section is the same rate constant or cross section, no matter how one looks at it. But a velocity, an angle, or even an intensity can depend on how the detector or the experimenter views the situation. 

The assumption that the activation cross section varies with neutron energy as 1/v in the thermal neutron region is valid for most (n,y) reactions. The two reactions that deviate the most from the 1/v assumption are Lu(n,y) Lu (typically +0.4%/K) and Eu(n,y) Eu (typically —0.1%/K). The reaction rates for these two reactions, relative to a monitor reaction like Au(n,y) Au, will depend on the thermal neutron temperature in the irradiation channel used. A new set of equations, the Westcott formalism (Westcott 1955), was developed to account for these cases and used the Westcott g T ) factor, which is a measure of the variation of the effective thermal neutron activation cross-section relative to that of a 1/v reaction. In the modified Westcott formalism, the following differences are also included the Qo(a) value of the Hogdahl formalism is replaced by the So(< ) value, and the thermal to epithermal flux ratio, f, is replaced by the modified spectral index, r a) TJTo). To use this formalism with the kg method (De Corte et al. 1994), it is necessary to measure the neutron temperature, r , for each irradiation and a Lu temperature monitor should be irradiated. The Westcott formalism needs to be implemented only when analyzing for Lu and Eu. There are several other non-1/v nuclides Rh, In, Dy, Ir, and Ir, but for these the error... 

The shear stress for this approach corresponds with that of the rectangular channel (equation (18)). The above relation simply approximates the rectangular cross-section as a circle, and uses the shear rate equation for the circular channel. We also present the flow curves thus obtained in Fig. 5. The flow curve for the square die is in good agreement with that of the capillary die. The other rectangular dies produce large errors. Therefore, the above relation is only valid for dies having a square cross-section (i.e. H=W). 

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