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