FIGURE 4.2 Generalized sensitivity analysis

Application of Uncertainty Analysis to Ecological Risk of Pesticides 

Hornberger and Spear s original application of generalized sensitivity analysis (GSA) used a binary acceptance-rejection procedure, i.e., they discarded a Monte Carlo realization if they thought that the prediction was inconsistent with the site-specific data (a nonbehavior ) or kept it if they thought it was consistent (a behavior ). The prior probability on each Monte Carlo realization was the reciprocal of the total number of realizations. After the acceptance-rejection procedure was applied, the updated (posterior) probability on each realization that was classified as a behavior was the reciprocal of the number of behaviors, and the posterior probability on nonbehaviors was zero. 

By Bayes s rule, the posterior probability on a Monte Carlo realization of a model equals the probability of observing the site-specific output data if the realization is correct, times the prior probability that the realization is correct, normalized such that the sum of the posterior probabilities of the Monte Carlo realizations equals 1. In Monte Carlo analysis, all realizations are equally likely (i.e., the pritM probability on each realization of an n-realization Monte Carlo simulation is 1/n). Therefore, the BMC acceptance-rejection procedure boils down to the following The probability that a model realization is correct, given new data, equals the relative likelihood of the having observed the new data if the realization is correct. 

The posterior probabilities on the Monte Carlo realizations of the model are determined by the error structure in the data. 

Consider, for example, a model that is being used to predict the log-concentration of a chemical in some environmental medium (e.g., the average log-transformed concentration in the muscle tissue of fish exposed to the chemical at a particular site). 

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One approach to sensitivity analysis for two variables considered simultaneously is to construct a three-dimensional graph with the x and y axes representing the two variables and the z axis serving as the figure of merit. The combined function is now a surface and we now have a break-even line. But three-dimensional graphs are difficult to construct and generally harder to interpret. A useful... 

Because the ternary diagram demonstrates only the thermodynamic potential, the gasifier models were used to carry out a sensitivity analysis of the ash content. Figure 7.14a and b show the results for cold gas efficiency, which are, in general, consistent with the observations from Figure 7.13a. Regarding the... 

Figure 2 shows the results of CE-SDS separation of a protein using a short capillary (33.0 cm total) and a long capillary (48.5 cm total). The analysis using the long capillary takes more time and shows decreased sensitivity. The short capillary is generally preferred, since it requires less analysis time and produces better sensitivity. 

Figure 13.2 Table of activation analysis sensitivities as offered by General Atomic Company, San Diego, California.

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