Apparent error

Two methods are used to evaluate the predictive ability for LDA and for all other classification techniques. One method consists of dividing the objects of the whole data set into two subsets, the training and the prediction or evaluation set. The objects of the training set are used to obtain the covariance matrix and the discriminant scores. Then, the objects of the training set are classified, so obtaining the apparent error rate and the classification ability, and the objects of the evaluation set are classified to obtain the actual error rate and the predictive ability. The subdivision into the training and prediction sets can be randomly repeated many times, and with different percentages of the objects in the two sets, to obtain a better estimate of the predictive ability. 

We find that our appioxunak atomic weight value yields a formula of M20,. which we know cannot be correct We also know that M20O29 is unreasonable What we perceive is that the formula is undoubtedly M2Ot anc tjjat tjje apparent error is undoubtedly caused by the approximate atomic weight Assuming that... 

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 ... 

With the number nwrong of misclassified samples from the training set the apparent error rate, A HR, is ... 

One may plot the data as shown in Figure 7 for water sprays and for a particulate spray (14). [A particulate spray is formed from a liquid imbibed in sized particles of a lightly crosshnked, swellable polymer.] Air (glass rod) and floor samples are treated separately because of the uncertain impaction efficiency on the rods, as previously discussed. The large apparent error for the particulate spray data of Figure 7b results from the proximity to the detection limits of the analytical method used. 

This table shows two things. First, this is a very precise instrument as for reasonable masses the apparent error is well below 1%. Second, not surprisingly, the relative errors become less as the magnitude of the quantity being measured increases. Thus it is always desirable to measure as large a quantity as possible if circumstances allow. 

Experimental data of Mohnke and Saffert, Reference 17. [During the verification of the data in this paper an apparent error was found in Mohnke and Saffert s paper (17). If the respective retention times are correct, the a for o,p-H2 at GT.S K. should be 1.40 rather than 1.653. This error also appeared in Katorski and White s paper (16) and since the succeeding S values in that paper (16) were computed from the a for o,p-H2, all values for S at GT.S K. in Table IV of Reference 16 are incorrect. The correct values appear in Table III of the current paper.]... 

Often it is necessary to say no material found. This is a source of satisfaction to the patent attorney in the case of patentability searches, but never to the library staff The original articles are not sent with the report, but are available to the patent attorney upon request. The reports are not critical, except for the fact that apparent errors are noted. 

The results of classification techniques examined in this chapter will be assessed by their apparent error rates using all available data for both training and vahdation, in line with most commercial software. 

Apparent error, of classification, 126 Artificial neural networks, 147 Assiociation coefficients, 96... 

The reader may detect an apparent error in nomenclature here. Pole 5 for example, is assumed to be a 100 pole and spot 5 on the diffraction pattern is assumed, tacitly, to be due to a 100 reflection. But aluminum is face-centered cubic and we know that there is no 100 reflection from such a lattice, since hkl must be unmixed for diffraction to occur. Actually, spot 5, if our assumption is correct, is due to overlapping reflections from the 200, 400, 600, etc., planes. But these planes are all parallel and are represented on the stereographic projection by one pole, which is conventionally referred to as 100). The corresponding diffraction spot is also called, conventionally but loosely, the 100 spot. 

Values of Yq are often taken to be the surface tension of the pure components, Y and have also been obtained by iterative procedures. Figure 4a shows a typical plot of Y as a function of x for a binary slag and the individual x Yi contributions have also been included. These methods work well for certain slag mixtures but break down when surface-active constituents, such as P205 are present. These components migrate preferentially to the surface and cause a sharp decrease in the surface tension and consequently only very small concentrations are required to cause an appreciable decrease in Y. Thus some unreported or undetected impurity could have a marked effect on the surface tension of the slag and thereby produce an apparent error in the value estimated by the model. In this respect surface tension differs from all the other physical properties which are essentially bulk properties. 

Of interest here is how well a model will predict some future response in some external or new data. One may look at the average residual error in the data set from which the prediction rule was estimated, called the apparent error rate. However, this estimate of the residual error (apparent error here) will be too optimistic and will underestimate the true prediction error. The problem here is that the training and assessment sample are the same. CV is used to correct this underestimation of the apparent error rate. 

The double bootstrap was a method originally suggested by Efron (15) as a way to improve on the bootstrap bias correction of the apparent error rate of a linear discrimination rule. It is simply a bootstrap iteration (i.e., taking resamples from each bootstrap resample). The double bootstrap has been useful in improving the accuracy of confidence intervals but it substantially increases computation time and most likely increases the incidence of unsuccessfully terminated runs. It has been applied to linear models but not to PM modeling. 

For objective data, especially when collected in an automated fashion, apply objective data cleaning criteria such as range checks and consistency comparisons. If apparent errors are found that are not simply transcription errors, delve deeply into the reasons and look for systematic errors such as incorrect units, miscalibrated devices, carelessness, or data fraud. 

Extensive documentation of the accuracy of molecular mechanics calculations has been reported.For the most part, the discrepancies between experimental and calculated molecular geometries are within experimental error. Many of the systematic discrepancies in MM2, for example, have been documented. Some of the apparent errors can be associated with incorrect comparisons of bond lengths that are defined differently in various experimental and computational methods. The bond lengths have different numerical values because they are different physical quantities, rather than being real errors. Other problems have been attributed to a lack of accurate experimental data when the force field equations and parameters were formulated. 

Table 1 shows the kind of results that can be obtained (from MM3) for a typical group of compounds (amines). (From ab initio calculations, it was concluded that the apparent error in diisopropylamine is due more to experimental error than to error in the calculation. )... 

Mixture of the sample gas with O2 N2 or a noninflammable gas will result in an apparent error on the positive side in the calorific value corresponding to the density and refractive index of the components. Table 3 gives a sample of errors produced using the data in Figures 1 and 5. 

In a commentary on both these papers, Erlenmeyer pointed out an apparent error that Kekule had committed in suggesting that unsaturated (free) affinities and double bonds are equivalent ideas, and lead to the same formulas. They aren t, and they don t. But he also had some critical comments for his other friend ... 

By comparison, it may appear unjustified to state that plastic failme criteria are usually defined in terms of critical strain (rather than stress), and, by comparison with metal, going from strain to stress may appear to be a limited analysis. This apparent error depends on recognition of the fact that stresses and strains are not as intimately related for URPs as they are for metals. This action is demonstrated by reviewing stress/ strain curves for typical URPs material. 

The TylG PKS enzyme consists of five multifunctional proteins that manipulate the nascent polyketide in an assembly line manner. Each chain extension event is catalyzed by a discrete module of catalytic domains that selects the incoming acyl-CoA extender unit, catalyzes decarboxylative condensation, and determines the reductive state of the newly incorporated unit. Finally, since nascent polyketides are attached to the enzyme as thioesters, the PKS component that catalyzes the final round of chain extension, TylGV, possesses a carboxy-terminal TE domain that terminates chain extension and cyclizes the product by esterification between the C-1 carboxyl group and the C-15 hydroxyl group. Type I PKS enzymes are apparently error-prone and are assisted by editing TEs. These are encoded by orfs adjacent to the PKS genes in macrolide producers and are proposed to remove aberrant materials that would otherwise block the PKS enzymes. Thus, disruption of tylO in S. fradiae reduces tylosin production by at least 85% [103]. 

Van Gisbergen et have also noted an apparent error in the DFT formulae which lead to unreasonable results for computed optical properties. 

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