Parameter-uncertainty ratio

Local sensitivity analysis is of limited value when the chemical system is non-linear. In this case global methods, which vary the parameters over the range of their possible values, are preferable. Two global uncertainty methods have been used in this work, a screening method, the so-called Morris One-At-A-Time (MOAT) analysis and a Monte Carlo analysis with Latin Hypercube Sampling (Saltelli et al., 2000 Zador et al., submitted, 20041). The analyses were performed by varying rate parameters, branching ratios and constrained concentrations within their uncertainty interval,... 

The first widely used global method was the Fourier Amplitude Sensitivity Test (FAST) (for a review see [83]). In the FAST method, all rate parameters were simultaneously perturbed by sine functions with incommensurate frequencies. Fourier analysis of the solution of the model provided the variance crf(t) of concentration i, and also the variance o- (t) of c, arising from the uncertainty in the /th parameter. Their ratio... 

The normalized sensitivity index of the residual to a parametric uncertainty Si is the ratio between effort (or flow) given by the uncertainty 5, and the effort (or flow) contributed by all the parameter uncertainties a. Thus, the sum of these indices gives... 

The purpose of this exercise is to identify what parameters need to be further investigated if the current range of uncertainty in reserves is too great to commit to a development. In this example, the engineer may recommend more appraisal wells or better definition seismic to reduce the uncertainty in the reservoir area and the net-to-gross ratio, plus a more detailed study of the development mechanism to refine the understanding of the recovery factor. Afluid properties study to reduce uncertainty in (linked to the shrinkage... 

Once values for R , Rp, and AEg are calculated at a given strain, the np product is extracted and individual values for n and p are determined from Eq. (4.19). The conductivity can then be calculated from eq. (4.18) after the mobilities are calculated. The hole mobility is the principal uncertainty since it has only been measured at small strains. In order to fit data obtained from elastic shock-loading experiments, a hole-mobility cutoff ratio is used as a parameter along with an unknown shear deformation potential. A best fit is then determined from the data for the cutoff ratio and the deformation potential. 

Example 57 The three files can be used to assess the risk structure for a given set of parameters and either four, five, or six repeat measurements that go into the mean. At the bottom, there is an indicator that shows whether the 95% confidence limits on the mean are both within the set limits ( YES ) or not ( NO ). Now, for an uncertainty in the drug/weight ratio of 1%, a weight variability of 2%, a measurement uncertainty of 0.4%, and fi 3.5% from the nearest specification limit, the ratio of OOS measurements associated with YES as opposed to those associated with NO was found to be 0 50 (n == 4), 11 39 (n = 5), respectively 24 26 (u = 6). This nicely illustrates that it is possible for a mean to be definitely inside some limit and to have individual measurements outside the same limit purely by chance. In a simulation on the basis of 1000 sets of n - 4 numbers e ND(0, 1), the Xmean. Sx, and CL(Xmean) were calculated, and the results were categorized according to the following criteria ... 

Hence by assigning two parameters, a Q and an c, to each of a set of monomers, it should be possible according to this scheme to compute reactivity ratios ri and V2 for any pair. In consideration of the number of monomer pairs which may be selected from n monomers—about n /2—the advantages of such a scheme over copolymerization experiments on each pair are obvious. Price has assigned approximate values to Q and e for 31 monomers, based on copolymerization of 64 pairs. The latitude of uncertainty is unfortunately large assignment of more accurate values is hampered by lack of better experimental data. Approximate agreement between observed and predicted reactivity ratios is indicated, however. 

Since the uncertainty of the CHF predictions determines the safety margin of the protection systems and control systems for limiting the operating power of a reactor, the critical power ratio evaluated in (a) or (b) represents a realistic parameter for ensuring a proper safety margin. The simple CHF ratio as defined in (c) is rather too optimistic from a reactor safety point of view. 

The biorefinery industry is marked with a feedstock related to the dispersed nature of its diet. The incoming raw material to a biorefinery is produced in a small scale (compared to an oil refinery), and in remote, distributed locations. Consequently, the biorefinery capacity is a parameter difficult to define due to the uncertainty in collection and blending of the feedstock. The next question is to what extent will the oil industry be involved in such operations and how will that affect the fossil to renewable ratio or the intake feedstock. 

Comparison of GCE model parameters with production ratio data from the literature Tq = 9.9 3.5 Gyr. The high uncertainty reflects the difficulties of estimating theoretically the production ratio of r-process elements, whose production sites are not well known. 

The most convincing evidence for the BC model of Mu in III-V materials comes from the nuclear hyperfine structure in GaAs. The hyperfine parameters for the nearest-neighbor Ga and As on the Mu symmetry axis and the corresponding s and p densities are given in Table I. One finds a total spin density on the As(Ga) of 0.45 (0.38) with the ratio of p to 5 density of 23 (4) respectively. The fact that 83% of the spin density is on the two nearest-neighbor nuclei on the Mu symmetry axis agrees with the expectations of the BC model. From the ratios of p to s one can estimate that the As and Ga are displaced 0.65 (17) A and 0.14(6) A, respectively, away from the bond center. The uncertainties of these estimates were calculated from spin polarization effects, which are not known accurately, and they do not reflect any systematic uncertainties in the approximation. These displacements imply an increase in the Ga—As bond of about 32 (7)%, which is similar to calculated lattice distortions for Mu in diamond (Claxton et al., 1986 Estle et al., 1986 Estle et al., 1987) and Si (Estreicher, 1987). 

CNcrit, included in the calculation of critical nitrogen leaching, Ni(crit), values, the input of this endpoint parameter into the uncertainty of CL(N) is expressed in a lesser degree. Furthermore, the runoff processes are practically not significant for ecosystems of Luvic Phaeozems, Chernozems and Kashtanozems due to low P PE ratio. During the calculations of CL(N) for ecosystems of North East Asia, the values of critical immobilization and denitrification from N depositions as the endpoints both in relative and absolute meanings played a subordinate role that obviously reflects their minor contribution into uncertainty and sensitivity analysis of the computed output values of ecosystem sensitivity to acidic deposition. 

In some papers, only the spin-allowed bands have been used in the analysis for d3 and d8 systems, this obviates the need to consider the Racah parameter C. Where the spin-forbidden bands have been included, C has sometimes been allowed to find a value which best fits the experimental data, along with the other parameters others have assumed a fixed value of the ratio B/C, such as 0.2S. The treatment of interelectron repulsion introduces some uncertainty into the orbital splitting parameters. Although it is well-known that the d-d spectra of Oh chromophores cannot be perfectly fitted within a model which allows only one value of B (1-3,... 

Renwick (1991, 1993) analyzed interindividual differences of healthy volunteers by comparing the maximum and mean values of pharmacokinetic parameters (7 substances) and pharmacodynamic parameters (6 substances). The data indicated that toxicokinetic differences were slightly greater than toxicodynamic differences. With one exception, the ratios between the maximum and mean value for a substance s kinetic parameter ranged from 1.8 to 4.2 with most values between 3 and 4, and it was concluded that a factor of 3-4 would be sufficient to consider toxicokinetic differences for 99% of the healthy, adult population and for 80% of the substances. The ratios between the maximum and mean value for a substance s dynamic parameter ranged from 1.5 to 6.9 with most values between 1.7 and 2.7. Based on the analyses, Renwick proposed to subdivide the interindividual factor of 10 into a factor of 4 for pharmacokinetic differences and a factor of 2.5 for pharmacodynamic differences. The aim of the subdivision of the 10-fold factor was to allow the incorporation of suitable compound-specific data for one particular aspect of uncertainty. 

In addition to addressing stochastic uncertainty, one may want to address uncertainty related to parameters measured without variation (e.g., unit cost estimates, discount rates, etc.), whether or not the results are generalizable to settings other than those studied in the trial, and, for chronic therapies, whether the cost-effectiveness ratio observed within the trial is likely to be representative of the ratio that would have been observed if the trial had been conducted for a longer period. These sources of uncertainty are often addressed using sensitivity analysis. 

One possible reason of such a discrepancy is that during regression fitting an experimental uncertainty may spread over various parameters, thus leading to somewhat distorted final picture. Probably, a more reliable way to measure similarity/dissimilarity of solvents would be to rely on the direct experimental measurements of the distribution ratios rather than on the derived quantities, that is, LSFER parameters. The present authors employed that approach [15]. 

We have just shown that, within exptl uncertainty, the Gurney approach leads to values of r that are in good accord with Ps obtained from Pj measurements. We now wish to examine how the approach of Aziz et al (Ref 3) which appears to be on sounder theoretical grounds than the Gurney treatment, relates to observed detonation parameters. The comparison between theory and expt is best performed in terms of the dimensionless ration V/D, a quantity for which Aziz et al obtain explicit and numerical solutions in terms of m/c and P This comparison is made in Fig 16, which presents theoretical and exptl V/D ratios as a function of m/c... 

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