Maximum 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,... 

The effect of NO exposure time on the time at which the N2 and N2O signals attain a maximum is shown in Fig. 16. It is seen that the model of NO reduction predicts that N2 formation peaks about 0.5 s after the peak in the N2O formation and that the peak times for both products decline by about 0.5 s as the NO exposure time is increased from 5 to 30 s. These trends are in good agreement with the data. It should be noted that since a product analysis could be taken only once every 0.5 s, it was not possible to determine product peak positions with an accuracy of better than 0.5 s. Consequently, both the predicted difference between... 

Use of dynamic reactions docs make a noticeable difference in the maximum predicted response which would permit adjustment of sizes tf desired. 

The most extensive test which has been made of this conduction model for thermal explosion is to be found in the work of Vanp e on the explosion of CH2O + O2 mixtures. He used a calibrated thread of 10 per cent Rh-Pt alloy of 20 m diameter (jacketed by a 50-m quartz sleeve) suspended at the center of a cylindrical vessel to measure directly his reaction temperature during the induction periods preceding explosion. By Uvsing He and Ar as additives and vessels of different diameters he was able to verify the dependence of the critical explosion limits on vessel size and on thermal conductivity of the gas mixture. In addition, he was able to check the maximum predicted temperature at the center of the vessel just prior to explosion and also the value of 8c = 2 [Eq. (XIV.3.12)], the critical explosion parameter for cylindrical vessels. Finally, with a high-speed camera, he was able to show directly that the explosions in this system do start at the center, the hottest region, " and propagate to the walls. 

The modelling results of the temperature distribution in cellulose samples during TGA experiments are displayed in Figures 1 - 3. At a constant heating rate of 108 K/min, the temperature in the interior of a cellulose sample of 1 mg follows the temperature of the sample surface closely with a maximum temperature difference of less than 0.15 K between the different spatial layers of the cellulose sample (Fig. 1). Under the same conditions, the spatial layers of a cellulose sample of 3 mg exhibit a maximum temperature difference of 0.8 K (Fig. 2). This is mainly due to unsatisfied heat demands of the endothermic reaction, since a similar calculation with ArH = 0 kj/mol yielded a maximum temperature difference of 0.2 K between the different spatial layers of the cellulose sample. In a cellulose sample of 20 mg at a constant heating rate of 108 K/min, a maximum temperature difference of nearly 25 K is predicted between the different spatial layers of the cellulose sample (Fig. 3). It is evident that such sample sizes are unsuitable for kinetic analyses applying the assumption of a homogeneous sample temperature, as stated in the literature before... 

As shown in Table XXVII, the maximum predicted splittings of the amide I mode vary with the conformation of the turn (a result of differences in the TDC contributions). On the basis of the observed splitting of 50 cm, conformations 3, 8, 9, and 10 could be considered possible ones, although the frequencies of 3 are in better agreement with observed bands of the solid (Fig. 29a). For amide II, observed IR bands... 

It turns out that the 100-m reactor is grossly oversized. The boldface values in Table 6.2 show a valley in the V — T plane where the annualized unit cost rounds to 2.30 kg . Marketing is somewhat relieved. A more detailed search shows what appears to be a minimum aty = 12m andr = 379 K with an associated cost of 2.3001 kg . Within the boldface area, the maximum cost difference is about 0,005 kg . At a production rate of 50,000,000 kg y, the annual cost difference would be 250,000. However, do not take this number too seriously. An economic prediction accurate to 0,005 kg is unrealistic for anything but an operating plant. There is model error, and there are other factors to consider before a design choice is made. 

Although the designs have low variance inflation factors, they are not rotatable, often showing considerable deviations from the property. Also as a general rule the saturated or almost saturated designs show considerable differences in the variance of prediction over the domain. The maximum prediction variance function in the (hyper-)cube can be high (d > 1.8). 

Although little is known concerning the identity of the transition state for these iodide induced reactions, the strict adherence to anti stereospecificity indicates the importance of rr-orbital overlap and a high degree of double bond character seems probable. The 6-fold rate difference (almost the maximum predicted from eclipsing of methyl substituents) between the rates of formation of Irani-and c/i-2-butenes from 2.3-dibromobutane supports this hypothesis -. ... 

The predicted bed temperature profiles at different times during the production step are shown in Fig. 9. A maximum temperature difference of about 7°C is observed near the bed center. It can be seen that during the cycle the profiles seem to shift vertically throughout the bed. 

The occupied bands are called valence bands the empty bands are called conduction bands. The top of tire valence band is usually taken as energy zero. The lowest conduction band has a minimum along the A direction the highest occupied valence band has a maximum at F. Semiconductors which have the highest occupied k -state and lowest empty state at different points are called indirect gap semiconductors. If k = k, the semiconductor is call direct gap semiconductor. Gennanium is also an indirect gap semiconductor whereas GaAs has a direct gap. It is not easy to predict whether a given semiconductor will have a direct gap or not. 

In so doing, we obtain the condition of maximum probability (or, more properly, minimum probable prediction error) for the entire distribution of events, that is, the most probable distribution. The minimization condition [condition (3-4)] requires that the sum of squares of the differences between p and all of the values xi be simultaneously as small as possible. We cannot change the xi, which are experimental measurements, so the problem becomes one of selecting the value of p that best satisfies condition (3-4). It is reasonable to suppose that p, subject to the minimization condition, will be the arithmetic mean, x = )/ > provided that... 

In this project, we shall predict the wavelength of the absorption maxima of the same four polyenes using the calculated difference (in units of eV), between the LUMO and HOMO of these four molecules (Fig. 8-6). Bear in mind that this is not an ab initio calculation of wavelengths of maximum absorption, because empirically fitted parameters, Yio exist within the program or are... 

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