Handling Correlated Inputs Within Global Uncertainty and Sensitivity Studies

6 Handling Correlated Inputs Within Global Uncertainty and Sensitivity Studies 

As discussed in Sect. 5.6.2, a full evaluation of the input uncertainties to a model should, where relevant, provide information on the correlations between input parameters. This can be represented through the joint probability distribution of the parameters or through a covariance matrix Sp such as that shown in Eq. (5.68). The joint probability distribution of model parameters can be determined from experimental data using the Bayes method (Berger 1985). Kraft et al. (Smallbone et al. 2010 Mosbach et al. 2014), Braman et al. (2013) and Miki et al. (Panes et al. 2012 Miki et al. 2013) have calculated the p of rate parameters from experimental data. The covariance matrix of the rate parameters was calculated from the back propagation of experimental errors to the uncertainty of parameters by Sheen et al. (Sheen et al. 2009,2013 Sheen and Wang 201 la, b) and by [Turanyi 

Here p is a matrix of the mean values for each parameter. As discussed in Sect. 5.6.2, accounting for correlations between parameters is important if significant off-diagonal terms are present in the covariance matrix, since, otherwise, an overestimation of the width of the predicted output distributions can occur. 

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