Since the above term is always equal to zero, the estimated covariance matrix $\u2211$ is not defined and we cannot assign a parametric uncertainty. Since we have prior information about the scale, the actual error lies between 1% and 2%; we can use the Bayesian approach as described in Refs. ^{2} and ^{9} under the premise that the prior information can be expressed in terms of normal distributions. The prior information on the parameter $\kappa $ is treated as an additional data point the model function has to account for, such that we have a function that still depends on $\kappa $ and $x$ but now maps into an ($m+1$)-dimensional space, with the ($m+1$)’th value simply being $\kappa $. This also adds additional terms to the Jacobian, $Jm+1,1=(\u2202/\u2202\kappa )\kappa =1$ and $Jm+1,2=(\u2202/\u2202x)\kappa =0$, such that Display Formula
$F\u02dc:R2\u2192Rm+1,F\u02dc(\kappa ,x)=[F(\kappa ,x),\kappa ]T,andJm+1,1=1,Jm+1,2=0.$(17)