Parameter sensitivity analysis plots

Fig. 11.17 Parameter sensitivity analysis plots (2D and 1D marginal posterior distribution plots for all parameters). (From S. Sahin, J. Warna, P. Maki-Arvela, T. Salmi, D.Yu. Murzin, Kinetic modelling of lipase-mediated one-pot chemo-bio cascade synthesis of R-1-phenyl ethyl acetate starting from acetophenone, J. Chem. Technol. Biotechnol. 85 (2010) 192-198. Copyright 2010 Wiley).

Figure 2. Sensitivity analysis plotting each input parameter to the estimate of risk based on that parameter. The reason differs for Nq is that the sensitivity analysis is made on the outer instead of the inner two dimensional Monte Carlo loop.

The results of a sensitivity analysis are usually presented as plots of an economic criterion such as NPV or DCFROR vs. the parameter studied. Several plots are sometimes shown on the same graph using a scale from 0.5 x base value to 2 x base value as the abscissa. 

When a model is used for descriptive purposes, goodness-of-ht, reliability, and stability, the components of model evaluation must be assessed. Model evaluation should be done in a manner consistent with the intended application of the PM model. The reliability of the analysis results can be checked by carefully examining diagnostic plots, key parameter estimates, standard errors, case deletion diagnostics (7-9), and/or sensitivity analysis as may seem appropriate. Conhdence intervals (standard errors) for parameters may be checked using nonparametric techniques, such as the jackknife and bootstrapping, or the prohle likelihood method. Model stability to determine whether the covariates in the PM model are those that should be tested for inclusion in the model can be checked using the bootstrap (9). 

ABSTRACT Within the EU project PAMINA different Sensitivity Analysis (SA) techniques have been applied to models that simulate the behaviour of different radioactive waste repositories. This paper summarises the main results and highlights specific aspects of regression/correlation techniques, the use of alternative imputation methods for datasets with missing values, the use of derived input parameters, the use of Monte Carlo filtering techniques in combination with cobweb plots and of variance based techniques. 

The behavior of the product formation model including such multiinhibition kinetics (with repression), basically represented in Fig. 5.47, is shown in sensitivity analysis in the qp/p plots of Fig. 11.25 through 11.29, with variations in all four parameters Xp, X,p, X,sp, and Xjsx-11. Evaluation of substrate feeding strategy for a fed-batch culture with optimal production of secondary metabolites—case study. On the basis of the mathematical model (Equs. II.24-II.29) and experimental estimation of model parameters, an optimal S feed can be found by simulations adding the expression Fs(t) for S feed to Equ. 11.25 ... 

Parameter estimation is typically followed by a statistical analysis of the parameters, which comprises the variances and confidence intervals of the parameters, correlation coefficients of parameter pairs, contour plots, and a sensitivity analysis. The confidence intervals of the parameters are obtained from standard statistical software the procedure is not treated in detail here. 

Fluorescence-based measurements are already very sensitive and widely used in bio-medical analysis. However, the metallic nanostructures provide further improvement on the sensitivity and limit of detections through the enhancement of the local field. Therefore, a large number of researchers are dedicated to developing substrates for SEFS [46-52]. The effect of the geometrical parameter of the nanostructure on the efficiency of the SEFS is well illustrated in Fig. 9. In this case, the SEFS enhancement factor (SEFS enhancement factor) is plotted against the periodicity of the arrays of nanoholes in gold films. The experiments were realized by spin-coating the arrays of nanoholes with a polystyrene film doped with the oxazine 720 [48]. 

The popularity of the Bode representation stems from its utility in circuits analysis. The phase angle plots are sensitive to system parameters and, therefore, provide a good means of comparing model to experiment. The modulus is much less... 

One of the most significant problems with the search for sensitivity predictors lies in the misuse of correlation analysis. It is a fundamental rule of statistical analysis that the data that are used to infer a correlation cannot be used to prove its existence. So if a study of these four substituted benzene compounds suggested that sensitivity is correlated with some spectroscopic transition or some bond parameter, then the existence of this correlation can only be proven by examining its validity using a large number of other materials not used to infer the correlation s existence. A true theory of sensitivity that resulted should be better than one which simply reaffirms the position of four compounds on a sensitivity plot—it should be equally able to tell us the relative sensitivities of new and different explosive compounds and in addition that nonexplosive compounds such as sodium chloride or liquid nitrogen will not explode. 

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