Model-Based Optimal Design of Experiments with Noninvertible Fisher Information Matrix

Abstract

In this thesis, different approaches are developed and compared to deal with a noninvertible Fisher Information Matrix (FIM) when designing sequential model-based (e.g., A, D, and V-optimal) experiments. Proposed approaches for dealing with this problem include: i) a “leave out” approach where problematic parameters are identified and left out of the design problem (LO approach), ii) a pseudo-inverse approach where the Moore Penrose pseudo inverse is used (PI approach), iii) an approach where modelers select new experiments based on their prior knowledge without using a formal experimental design technique (MS approach), a simple Bayesian approach that adds prior parameter knowledge to the FIM when designing experiments and therefore making it inventible. This study focuses on sequential A- and V-optimal design because these optimality criteria are relatively easy for modelers to interpret and are the most readily usable design criteria for situations where the FIM is noninvertible. Different case studies are investigated including two case studies involving production of pharmaceutical agents. The results for comparing LO, PI and MS approaches indicated that LO is the superior approach on average compared to two other approaches for both A- and V-optimal experiments. In addition, results indicated that, designing experiments using either LO or PI approaches are better than picking the corners of the design space as new experimental conditions, even for situations where the FIM is noninvertible. Next, a simple Bayesian approach is developed that adds the prior parameter knowledge to the FIM and makes in invertible for sequential MBDoE. Comparing the results of the Bayesian and LO approaches indicated that, the Bayesian approach is superior than the LO approach for MBDoE and the LO is better on average for parameter estimations.