Table 8 provides information about the user-specified prior parameter information used in three different Cases. The prior parameter guesses and corresponding standard deviations were used in the Bayesian objective function for parameter estimation (equation (6)). This prior information is also used in LO parameter estimation to obtain scaled sensitivity coefficients in Z (see equations (2) and (3)). As result, prior assumptions about parameters influence which parameters are estimated and which remained fixed at their initial values. The three cases described in Table 8 were used to investigate the influence of the prior parameter information on the quality of parameter estimates and experimental settings. For all three cases, parameter initial guess\({\hat{\theta}}_{j0}\) were selected randomly from normal distributions with true mean \(\theta_{j}\) and true standard deviation\(s_{\theta_{j}}\) (see Table 5). In Case I, the modeler specifies prior information that is quite accurate (i.e., prior parameter standard deviations are 1/5 of the true value), whereas in Case II, the modeler is less certain about the initial parameter guesses. The selection rules in the third column of Table 8 for Cases I and II prevent random selection of unrealistic negative parameter values and parameter values more than 3 standard deviations from the true parameter values. Case III is used to investigate whether the Bayesian or LO approach to MBDOE and parameter estimation is more robust to misinformed prior information (i.e., when modelers mistakenly believe that they know more about the plausible parameter values than is warranted). In Case III, initial parameter guesses are further from the true values than the modeler believes.

Table 8. Selection of parameter initial guesses from normal distributions