Mean absolute errors

After selection of descriptors/NN training, the best networks were applied to the prediction of 259 chemical shifts from 31 molecules (prediction set), which were not used for training. The mean absolute error obtained for the whole prediction set was 0.25 ppm, and for 90% of the cases the mean absolute error was 0.19 ppm. Some stereochemical effects could be correctly predicted. In terms of speed, the neural network method is very fast - the whole process to predict the NMR shifts of 30 protons in a molecule with 56 atoms, starting from an MDL Molfile, took less than 2 s on a common workstation. 

The accuracy of these methods is tested by finding the mean absolute error between the computed and experimental free energies of solvation. The SM4 method does well for neutral molecules in alkane solvents with a mean absolute error of 0.3 kcal/mol. For neutral molecules, the SM5 methods do very well with mean absolute errors in the 0.3 to 0.6 kcal/mol range, depending on the method and solvent. For ions, the SMI method seems to be most accurate with... 

The square root of the variance is the standard deviation. The mean absolute error MAE is... 

The root-mean-square error is the square root of the mean square error. Note that since the root-mean-square error involves the square of the differences, outliers have more influence on this statistic than on the mean absolute error. 

For sources having a large component of emissions from low-level sources, the simple Gifford-Hanna model given previously as Eq. (20-19), X = Cqju, works well, especially for long-term concentrations, such as annual ones. Using the derived coefficients of 225 for particulate matter and 50 for SO2, an analysis of residuals (measured minus estimated) of the dependent data sets (those used to determine the values of the coefficient C) of 29 cities for particulate matter and 20 cities for SOj and an independent data set of 15 cities for particulate matter is summarized in Table 20-1. For the dependent data sets, overestimates result. The standard deviations of the residuals and the mean absolute errors are about equal for particulates and sulfur dioxide. For the independent data set the mean residual shows... 

Which measure of scatter is likely to be larger, the mean absolute error or the root-mean-square error ... 

Heats of formation, molecular geometries, ionization potentials and dipole moments are calculated by the MNDO method for a large number of molecules. The MNDO results are compared with the corresponding MINDO/3 results on a statistical basis. For the properties investigated, the mean absolute errors in MNDO are uniformly smaller than those in MINDO/3 by a factor of about 2. Major improvements of MNDO over MINDO/3 are found for the heats of formation of unsaturated systems and molecules with NN bonds, for bond angles, for higher ionization potentials, and for dipole moments of compounds with heteroatoms. 

In this approximation the mean polarizability a is given in atomic units and h is the number of hydrogen atoms. They founda mean absolute error of 1.2% and... 

Figure 6-14. Average domain size vs. inverse deposition temperature Tor different film thicknesses. Error bars represent the mean absolute error and straight lines the best lit for each film thickness. Doited line is the locus of the transition from grains to lamellae. Data for 50-nm films are estimated from the correlation length of the topography fluctuations. Adapted from Ref. [501.

Figure 2.48 compares the predictions of this correlation with the flow boiling CHF data for water both in the rectangular micro-channel heat sink (Qu and Mudawar 2004) and in the circular mini/micro-channel heat sinks (Bowers and Mudawar 1994). The overall mean absolute error of 4% demonstrates its predictive capability for different fluids, circumferential heating conditions, channel geometries, channel sizes, and length-to-diameter ratios. 

The predictive capability of the proposed correlation for all operating conditions of the study by Qu and Mudawar (2003a) was illustrated. The mean absolute error (MAE) of each correlation... 

For a normal (Gaussian) error distribution, the RMSE is by a factor of Jl larger than the mean absolute error, also denoted as mean unsigned error. The error distribution of log Sw prediction methods appears to be somewhat less inhomogeneous than a Gaussian distribution and typically leads to a ratio of RMSE/mean absolute error... 

Note d and d denote mean and mean absolute errors, respectively, relative to the experiment, m, c, and R2 denote the gradient, intercept, and correlation parameters, respectively, of the correlation plots, relative to the experiment. 

As expected from our previous discussion of the CCSD valence correlation energies, the convergence towards the experimental energies is slow, with mean absolute errors of 511, 163, 61, 28, and 17 kJ/mol as... 

Table 1.12 Statistical measures of errors for extrapolated CCSD(T) AEs relative to experiment (kJ/mol). A is the mean error, Astd is the standard deviation around the mean error, Aabs is the mean absolute error, and Amax is the maximum absolute error.

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