Total sensitivity index

The total effect of parameter j can be defined as the sum of all sensitivity indices in which parameter j is present. Assume that we have three parameters a, b and c. The total sensitivity index of parameter a is defined as... 

The total sensitivity index characterises the additivity of the parameters (Homma and Saltelh 1996 SaltelH et al. 2010). If the parameters are totally additive, which... 

Liidtke et al. (2007) developed a new version of the method above that they call information-theoretic sensitivity analysis. Here the model is considered as a communication channel , which is a transmitter of information between inputs and outputs. Instead of analysing the variance of the ouQjut distribution, they measured output xmcertainty in terms of Shannon s entropy. The first-order sensitivity index, the higher-order sensitivity indices and the total sensitivity index aU have information-theoretic coxmterparts. 

Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., Tarantola, S. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comp. Phys. Commun. 181, 259-270 (2010)... 

The above measurement results also included the error contribution of the temperature cross-sensitivity of the device. From Fig. 7.11, the temperature dependence of the device was 0.074 nm °C Based on (7.6), the temperature crosssensitivity of the device was less than 3.2 x 10 6 RIU °C. Therefore, the total temperature cross-sensitivity-induced measurement error was about 2.8 x 10 4 RIU in Fig. 7.13 over the temperature variation of 87°C. The temperature dependence of the device was small and contributed only about 2.3% to the total refractive index variation over the entire temperature range. 

Whole blood total thiamin below 150 nmol per L is considered to indicate deficiency. However, the changes observed in depletion studies are small. Even in patients with frank beriberi, the total thiamin concentration in erythrocytes is only 20% lower than normal whole blood thiamin is not a sensitive index of status. 

The Gyna-ir Correlation can be sharpened by the two-phase argument. With the crosslinking agents confined to their own phase, the quantity of gel should be determined by the total surface area of that phase and, hence, the dispersion of the E/ABP in the polyethylene matrix. If we assume that better blending is achieved by matching the component melt viscosities, then Qninv should be dependent on the sensitizer melt index (MI), the relative volumes of the components -blend ratio, BR - and the total sensitizer concentration (Co). From least squares analyses of our results, we find ... 

A probabilistic measure of the sensitivity is represented by the variance of the error hAB due to the variation of a model parameter This quantity may be seen as the total effect of Gj/, which measures the uncertainty in Iiab that is unexplained after having learnt everything except G /. The variances Og and o of the error, corresponding to prior and posterior samples, are evaluated for each ratio RAB(id r, s), by replacing the vector Oj with O , and then are used to assess the relative influence of each parameter. As indicated in (Sibilio c Ciampoli 2006, Sibilio et al. 2006), Og can be interpreted as a global sensitivity index and the total effect of the considered parameter Oj can be interpreted as a local sensitivity index. 

Nutritional status assessment for thiamine is generally carried out by assaying the total thiamine in whole blood or erythrocytes, or by measuring the activity of erythrocyte transketolase before and after incubation with exogenous thiamine pyrophosphate. The latter serves as the sensitive index of thiamine nutritional status (Brin 1980). In addition to the enzymatic test, a measure of urinary thiamine in relation to dietary intake has been the basis for balance studies to assess the adequacy of intake. When thiamine excretion is low, a larger portion of the test dose is retained, indicating a tissue s need for thiamine. A high excretion indicates tissue saturation. In the deficient state, excretion drops to zero. Plasma pyruvate and lactate concentrations have also been used to assess thiamine status. 

Since the refractive index of an organic substance, such as a surfactant, is different from that of water it should in principle be possible to determine the surfactant concentration through measurement of the refractive index of the solution. This is indeed a feasible way. However, the method suffers from the drawback that it is not specific. Thus, small amounts of organic material will contribute to the total refractive index of the solution. Since surfactant concentrations are normally very low, small amounts of impurities will cause large variations in the measured surfactant concentration. Furthermore, the adsorbed amount is obtained as the difference between two measured concentrations (equation (22.9)) and is thus very sensitive to variations in the determined concentrations. One such source of organic impurity was mentioned previously - this is the material that is leaked from cellulose acetate filters when separating the particles from the solution by filtration. Thus, the nonspecificity of this approach renders it less attractive as a method to determine the adsorption through depletion of surfactants in the solution. 

Table 13.18. Evolution of the pinking sensitivity index in the same wine aged on fine lees and on total lees (Lavigne, unpublished results)...

This measure shows the fraction of the total variance of 7, which is reduced when the value of Xj is held at a fixed value and is therefore a measure of the influence of uncertainty in Xj. The first-order sensitivity index is between 0 and 1, although sometimes this is multiplied by 100 yielding 5)(,)%. The calculation of the integrals in Eq. (5.25) is nontrivial and the use of a Monte Carlo sampling method is described in Saltelli (2002) requiring N (2 m+1) model runs where N is the sample size chosen for the Monte Carlo estimates. 

This second-order sensitivity index shows the fraction of the total variance of 7, which is reduced when two parameters xj and x/ are fixed. In other words, the second-order sensitivity index characterises the interaction of the corresponding parameters. The sensitivity indices can be calculated up to an arbitrary n-th order by keeping n parameters fixed, but the computational time requirement increases exponentially with the order. 

The findings from TOTAL, n-d-M, and API are summarized in Table 2-10. The comparison illustrates how sensitive the predicted feed composition is to the refractive index 20°C. For instance, using the TOTAL correlation, there is a 35% drop in the aromatic content in using RIpo) = 1.5000 instead of RI(2o> = L5105. When using these correlations, every effort should be made to obtain accurate and consistent values for the refractive index at 20°C. With the refractive... 

Since ATP is present in ah organisms with a fairly constant intercellular concentration, the ATP concentration is a useful index of total biomass and has been applied as such to monitor bacteria in food, biomass in wastewater, and sewage sludge [160], The high sensitivity of this assay allows the use of the firefly assay as a tool for detection of life on other planets. Table 2 shows some applications of the analysis of ATP. 

The detection limit of the microresonator-based refractive index sensing device is directly related to the g-factor of the resonator and the sensitivity of the resonant mode discussed above. The g-factor of a microtube resonator is determined by the total loss of a resonant mode, including radiation loss, absorption loss, and surface roughness scattering loss. The overall g-factor can be expressed as... 

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