Scale-error

Systematic Errors.—Scale Errors. The error sources 1—3 mentioned in Table 2 give an error in the j-scale. Usually the error caused by the microdensitometer may be made negligible, but the determination of the electron wavelength (A) and of the nozzle-to-plate distance H) deserves further 

An error in the r-scale gives the same relative error in the mean amplitudes as in the distance parameters. The intensity expression contains the factor exp(— However, the relative errors in the u values are much 

Intensity Errors. A number of the error sources mentioned in Table 2 (especially 4—10) will leave the zero points in the molecular intensity function [equation (21)] almost unchanged, while the relative intensity values may be more seriously changed. Such errors will primarily affect the mean amplitudes of vibration. However, it should be emphasized that the correlation between some distances and amplitudes may be large in molecules with many nearly equal distances. Table 3 shows some of the correlation coefficients (c/. p. 45) in hexafluorobenzene. In such cases the distance parameters may also be affected to a large extent by these errors. 

The aperture angle of the sector may be measured with a microscope or derived from the scattering diagram of a well-known gas, say argon. The most critical region is, of course, close to the centre of the sector. With sufficient care the sector function may be determined quite accurately. 

To use photographic plate recording of the intensity data, the relationship for converting the optical density (Z)) to electron intensity must be known. The intensity seems to be directly proportional to the density below a certain D value which depends on the emulsion, usually about 0.6. The correction may be estimated by comparing plates recorded for the same compound, but with considerably different densities. In a structure determination it is usually possible to obtain plates with densities in a suitable range, say 0.1—0.9, where the correction is small. 

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Care needs to be taken if some components are present in trace quantities. If an estimated concentration is 0.5 ppm and the calculated value is 1 ppm, the scaled error is 100%. This is much too large an error for most variables and yet the absolute error might be acceptable for a trace component. In other situations, it might be necessary to define trace components with a high precision. A trace component threshold can be set, below which the convergence criterion is ignored. 

Buzzard, W., Instrument scale error study throws new light on flowmeter accuracy, Chemical Engineering, 66, pp. 147-50 (9 Mar 1959). 

The value of the expectation can also be used to scale errors when the covariance matrix Sy of the data vector is unknown. The usual procedure is to assume that Sy can be approximated by... 

Disadvantages come from the measurement error, which is driven not so much by the scale error as by the connecting tubing from the supply drum to the mix tank. This approach was practiced by Systems Chemistry, Inc. (now BOC), but has been replaced by other approaches. 

Radiation can also cause larger-scale errors involving many nucleotides. In some cases, the change in the chromosome is visible with a microscope (called chromosome aberrations). Some important types of chromosome aberrations are deletions, amplification, and translocation. Deletions are simply loss of a segment of DNA with the consequence... 

The values listed have been taken from Ref. since the parameters quoted in Ref. are flawed by a slight scale error in part of the intensity material ). 

The scale-error plot. By following the simple multiscale algorithm suggested above, a scale-error" plot is produced that can be used to make decisions about the optimal resolution level. 

The other useful information from the scale-error plot is that it will tell us something about the width of the features important to the prediction. If it is possible to create a very good model at very low resolution, this indicates that broad features are important for the prediction. If higher resolution is necessary to maintain good prediction, then this indicates the importance of narrow features in the data. 

The scale-error-complexity (SEC) surfaces. Instead of observing the prediction error with respect to resolution, it is also possible to monitor the complexity of the calibration/classification model. In PLS this can be measured by the number of PLS factors needed. How the error (e.g. RMSECV, RMSEP, PRESS) changes with varying the added scale and model complexity can be observed in scale-error-complexity (SEC) surfaces. In this case the first axis is the scales, the second axis is the model complexity (for PLS this is the number factors) and the third axis is the error. The complexity dimension is not limited to the number of PLS factors. For example classification and regression trees (CART) a measure based on tree depth and branching could be used [45],... 

Fig. 3. (a) Neutron-proton spin correlation parameter Cnn at 181 MeV. Predictions by the Nijmegen potential [13] (long dashes), the Paris potential [ 14] (dotted), and the Bonn full model [ 15] (solid line) are compared with the data (solid squares) from Indiana [18], The ( /datum for the fit of these data is 54.4 for Nijmegen, 3.22 for Paris, and 1.78 for Bonn. The experimental error bars include only systematics and statistics there is also a scale error of 8%. In the calculations of the all three error have been taken-into account [25]. (b) Same as (a), but at 220 MeV with the data from TRIUMF [19]. The z /datum for the fit of these data is 121.0 for the Nijmegen, 16.1 for the Paris, and 0.49 for the Bonn B potential [6]. In addition to the experimental error shown, there is a scale uncertainty of 5.5%. In the calculation of the all errors were taken into account [25]. 

Mean absolute scaled error (MASE) To overcome the drawbacks of existing measures, Hyndman and Koehler (2006) proposed MASE as the standard measure for comparing forecast accuracy across multiple time series after comparing various accuracy measures for univariate time-series forecasting. MASE is expressed as follows ... 

Twice the estimated standard errors including a possible scale error. 

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