A0754
Title: A sequential approach to obtain optimal designs for non-linear models harnessing closed-form solutions
Authors: Tirthankar Dasgupta - Rutgers University (United States) [presenting]
Suvrojit Ghosh - Rutgers University (United States)
Koulik Khamaru - Rutgers University (United States)
Abstract: D-Optimal designs for estimating parameters of response models are derived by maximizing the determinant of the Fisher information matrix, which depends on the unknown parameter vector of interest for non-linear models. Consequently, to obtain the D-optimal design for a non-linear model, one needs to have knowledge of the parameter to be estimated. One solution to this problem is to choose the design points sequentially, optimizing the D-optimality criterion using parameter estimates based on available data, followed by updating the parameter estimates using maximum likelihood estimation. On the other hand, there are many non-linear models for which closed-form results for D-optimal designs are available, but because such solutions involve the parameters to be estimated, they can only be used by substituting guestimates of parameters. A hybrid sequential strategy is proposed that replaces the optimization of the objective function at every single step by plugging in the estimates into the available closed-form solutions. Theoretical guarantees for the proposed approach are established. The usefulness of this approach in terms of saving computational time and achieving greater efficiency of estimation compared to the standard sequential approach is demonstrated with simulations conducted from two different sets of models motivated by real-life scenarios.
