Indicator errors

Even when the patterns are known to cluster, there remain difficult issues that must be addressed before a kernel-based approach can be used effectively. Two of the more fundamental conceptual issues are the number and size of clusters that should be used to characterize the pattern classes. These are issues for which there are no hard and fast answers. Despite the application of well-developed statistical methods, including squared-error indices and variance analysis, determining the number and size of clusters remains extremely formidable. 

Note Negative average error indicates that the correlation is conservative. The thermal diffusion coefficients of the reactor vendors proprietary grid geometries are not considered in this comparison. 

On the basis of extensive past analysis the iron content of an homogeneous ore sample is accepted to be 19.85%. An analysis of seven samples gave an average of 20.06% Fe. Within what probability levels is a determinate error indicated in the analysis if the absolute standard deviation of the results is 0.14% ... 

The sources of error indicated above were avoided in a series of experiments carried out by Donnan and Barker, which in principle resemble those made by Lewis, so that only a brief reference to them is necessary. The dissolved substance was nonylic acid, and a drop method. The results could be reproduced with very great accuracy, i.e., to a fraction of one drop in 300—500 drops. Adsorption was produced at a surface air-liquid, air being passed through the solution in bubbles of known size and number, so that the total active surface could be calculated. The bubbles, on reaching the surface, burst, hence the excess of solute carried by them remained in the surface very effective precautions were used to prevent diffusion backwards from this portion into... 

Measurement Residual Plot The statistical prediction errors indicate which samples have large spectral residuals. It can be instructive to then plot the residuals to diagnose the problem. In practice, only samples with large statistical prediction errors are examined, but all four will be plotted here. Tlte residuals for unknowns 1-4 are shown in Figures 5.20-5.23, respectively. Also shown are the measured and predicted responses. The residual for unknown 1 in Figure 5.20 resembles the model validation residuals shown in Figure 5.18. 

Statistical Prediction Errors (Model and Sample Diagnostic) From the S matrix it is possible to predict all four components (caustic, salt, water concentration, and temperature). However, in this application the interest is only in caustic and, therefore, only the results for this component are presented. The statistical prediction errors for the caustic concentration for the validation data vary from 0.006 to 0.028 wt.% (see Figure 5-54). The goal is to predict the caustic concentration to 0.1 wt.% (lo), and the statistical prediction errors indicate that the precision of the method is adequate. Also, there do not appear to be any sample(s) that have an unusual error when compared to the rest of the samples. 

Small values of this standard error indicate high reliability it is likely that the observed value, — X2, for the treatment effect is close to the true treatment effect, jLi — JL2- In contrast, a large value for the standard error tells us that — X2 is not a reliable estimate of [Xj — 1X2-... 

To view the error indicated by a green washer, double-click the LEFT mouse button on the washer ... 

Corrected to mid-period of sampling. Errors indicated are one standard deviation. Volumes are in meters3, STP. h Tr/( Tr -f Tb) = NbXb/NaXa. 

Partially Dehydrated Ba6 A. Full-matrix least-squares refinement was initiated using the atomic parameters of the framework atoms and of the barium ions (Ba(l), Ba(2), Ba(3), and Ba(4)) in fully hydrated Ba2+-exchanged zeolite A. Full anisotropic refinement converged to the error indices = 0.113 and R2 = 0.088. Simultaneously, the occupancy numbers at Ba(l),... 

PACF of the errors indicates a first-order autoregression component, therefore the parameter p is set to unity. The spikes at lags 13 and 25 are a consequence of the multiplicative seasonal model. 

The two data sets fall on a single curve (within experimental error), indicating that the fluid density is the prime factor in determining the value of n. The data for the other fluids was obtained under isothermal conditions. 

If none of the three relocations of the mobile point with respect to the centroid act to lower its squared error, then the program uses scaling to move all of the points away from the one with the least squared error. Scaling is useful to shake loose the simplex from a local minima, and allow it to propagate toward the absolute minima of squared error. Repeated scaling without any change in the point of lowest squared error indicates either that the solution has been found, or that the program could not break out of a local minima. 

TABLE 1 Lattice parameters of III-N compounds (hexagonal-wurtzite and cubic-zincblende structures). For GaN bulk crystals, the errors indicate variations between various samples, as the measurement accuracy was of about 5 parts per million. For cubic AIN and InN, the given lattice parameters are estimated from bond-lengths of the wurtzite phase. For all epitaxial layers, the given values are relaxed lattice parameters calculated from the measured ones using EQN (1),... 

The reaction error is thus expressed as a percentage of the total ion concentration. Positive reaction errors indicate cation excess negative errors indicate anion excess. Reaction errors are caused by the analytical errors of the individual parameters and the fact that not all possible ions are commonly measured. 

As stated, reaction errors are another way to estimate data quality (section 5.8). The reaction error can (and should) be better than 1%, but they are often larger. Many investigators will accept up to 5%. Using the latter criterion the reaction errors calculated in Table 5.6 (4.3%, 3.3%, 2.1%, 1.2%, and 1.6%) are acceptable. This example brings out a major shortcoming of the reaction error quality test the poor reproducibility of the S04 data, demonstrated above, is not reflected in the reaction error because SO4 is a minor compound of the Wisdom Spring water. Low reaction errors indicate acceptable quality of the data for the major ions alone. 

The mean accuracy of the computed potentials is + 0.08 V, and the reasonable linearity and the fact that the intercepts are identical within the error indicate that the neglected terms (solvation, entropy) are approximately dependent of the strain energies, as one might expect on simple qualitative considerations12311. 

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