Expected prediction difference

The model discrimination capability of a design can be measured by the differences between the predictions given by different models. This motivated Jones et al. (2005) to propose two criteria based on the differences of predictions the expected prediction difference and the maximum prediction difference. The expected prediction difference (EPD) is calculated as follows. Consider two models with model matrices X1 and X2 and hat matrices H1 and H2. Then, for any response y, the difference between two predictions is given by y1 —y2 = (H 1 — H2)y. The expected prediction difference measures the average distance between two fitted values over all possible normalised responses, where normalised means that the response vectory is scaled so that y y = 1.0. For any two model matrices X and X2,... 

Both the subspace angle and the expected prediction difference can be used to evaluate the model discrimination capability of a design d over a model space T. In Section 4, the selection of orthogonal designs using criteria based on these measures is discussed. 

In principle the use of the entropy of activation as a criterion is straightforward. The electrostatic contribution to this quantity, A5 i, for a reaction between two cations is predicted from simple electrostatic theory to be less than that for a reaction between an ion and a neutral molecule. If the reactions are otherwise similar, the overall entropies of activation can be expected to differ in the same way ... 

As there now exists a large body of laboratory studies on each of the variable systems, for example the effect of die lime/silica ratio in the slag on the desulphurization of liquid iron, the most appropriate phase compositions can be foreseen to some extent from these laboratory studies when attempting to optimize the complex indusuial process. The factorial uials are not therefore a shot in the dark , but should be designed to take into account die laboratory information. Any qualitative difference between die results of a factorial uial, and the expectations predicted from physico-chemical analysis might suggest the presence of a variable which is important, but which was not included in the nials. 

The success rate of every prediction set was greater than the value of 50% expected by chance. Specifically, the various sets of predictions differed from the 50% value by about 3 standard deviations (for the lowest success rate, which was for the merged data) to about 12 standard deviations (for the highest success rates, which were for the medium and long regions of disorder). Overall, these data provided very strong support for our hypothesis that disorder is encoded by the amino acid sequence (Romero et al., 1997b). 

The expected Cmax and AUC for each of the profiles are listed in Table 3. The profiles are predicted to show an acceptable range of Cmax values with around 20% difference between the fast and medium formulations and between the medium and slow formulations. The predicted differences in AUC are only related to the slightly different content of the three formulations, reflected in the Finf values (100% for the fast formulation and 102% for the other formulations). Normally, AUC is not expected to be rate-dependent unless there is some non-linear process involved in the disposition of the drug or drug release or absorption is very slow compared to gastrointestinal transit time. Given the predicted Cmax differences, these three formulations are appropriate choices for an IVIVC study as they show acceptable in vitro and predicted in vivo differences. 

Overall, this study indicated that generic simulation of pharmacokinetics at the lead optimization stage could be useful to predict differences in pharmacokinetic parameters of threefold or more based upon minimal measured input data. Fine discrimination of pharmacokinetics (less than twofold) should not be expected due to the uncertainty in the input data at the early stages. It is also apparent that verification of simulations with in vivo data for a few compounds of each new compound class was required to allow an assessment of the error in prediction and to identify invalid model assumptions. 

Absorption resonances resulting from excitation of surface modes are accompanied by scattering resonances at approximately the same frequencies this was pointed out following (12.26). In most experiments transmission is measured to determine extinction, which is nearly equal to absorption for sufficiently small particles. However, surface mode resonances have been observed in spectra of light scattered at 90° by very small particles of silver, copper, and gold produced by nucleation of vapor in an inert gas stream (Eversole and Broida, 1977). The scattering resonance peak was at 3670 A, near the expected position of the Frohlich mode, for the smallest silver particles. Although peak positions were predictable, differences in widths and shapes of the bands were concluded to be the result of nonsphericity. 

Would you expect the differences in properties for H2O and D2O to be larger or smaller than the differences in properties for D2O and T2O Do the data in Table 14.1 support your prediction ... 

It should be noted that, Model G and Model M predict quite different values of slip velocities, though their resolved structure may look similar, as shown by insets of Figure 5. Extending this seeming inconsistency to larger scales, we may expect that, simulations of real reactors with Model G and Model M may predict different solids flux even with similar impression of structures. Then, it is natural to question, which solution of these two models coincides with the reality. To answer this question, simulations of CFB risers are needed to test which will agree with experiments. 

Figure 6.7. Predictions of the diffuse gamma-ray emission of Coma as expected in different models for the CR origin bremsstrahlung for = 0.3 (short dashes) and 1 (long dashes) neutralino annihilation for Mx = 100 GeV (yellow area an enhancement factor 3 has been choosen) and p-p collision (blue area) (from ).

The stereochemistry of the reactions of vinyl cations with nucleophiles is predictably different depending on their geometry, (a) High stereospecificity is expected from bridged ions (trans addition to acetylenes and retention of configuration in substitution reactions of vinyl derivatives) and is experimentally observed in the case of thiirenium ions, (b) From free linear cations with two j3 substituents of equal size, complete racemization is expected and is fully verified in the substitution products from l,2-dianisyl-2-phenylvinylbromide (section II,C,2). 

While there appears to be some agreement between the observed and theoretical iron oxide solids settling velocities, the observed silicon oxide values appear to be several times greater than expected. This difference in behavior of the silicon oxide and iron oxide slurries cannot be accounted for by density effects. Since the ratio of the density of iron oxide and silica is 2.ll+, the predicted VgT for an iron oxide would be 3.8 times greater than for silica, Further work is needed to determine the critical characteristics of a solid that are important in governing its settling velocity. 

A second method involves the examination of residuals A residual is defined as the difference between an observed value and some expected, predicted or modelled value. If the suspect datum has a residual greater than, say, 4 times the residual standard deviation computed from all data, then it may be rejected. For the data in Table 6, the expected value is the mean of the ten results and the residuals are the differences betweeii each value and this mean. The standard deviation of these residuals is 14.00 and the residual for the suspected outlier, 49, is certainly less than 4 times this value and, hence, this... 

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