Conclusions
A simple Bayesian approach is proposed for the sequential model-based
design of experiments (MBDoE) when the FIM is noninvertible.
The results for the proposed Bayesian approach were compared with a
leave-out (LO) approach developed in previous studies. In addition, the
effectiveness of Bayesian and LO approaches for parameter estimation
were also compared, so that four different approaches were investigated
(i.e., Bayes-Bayes, LO-LO, Bayes-LO, and LO-Bayes) were investigated.
These approaches were tested using simulated data generated from a
7-parameter isothermal pharmaceutical production model and a
corresponding 14-parameter non-isothermal model. Three different cases
were considered wherein the modeler specified different prior
information about the parameters. The results indicate that the Bayes-LO
approach (i.e., a Bayesian approach for MBDoE combined with a LO
approach for parameter estimations) is superior to the three other
approaches. The proposed Bayesian approach for designing experiments
consistently provided superior experiments for use in parameter
estimation compared with the LO approach. However, after new
experimental data had been obtained, the LO approach for parameter
estimation consistently provided parameter values that were closer, on
average, to their true values than parameter estimates obtained from
Bayesian estimation. Promising simulation results obtained using
misspecified prior parameter knowledge indicated that the Bayes-LO
approach was somewhat robust to misinformation for the current case
study.