Date of Award:


Document Type:


Degree Name:

Master of Science (MS)


Mathematics and Statistics

Committee Chair(s)

Stephen J. Walsh


Stephen J. Walsh


Brennan Bean


Rong Pan


Experimental designs are used by scientists to allocate treatments such that statistical inference is appropriate. Most traditional experimental designs have mathematical properties that make them desirable under certain conditions. Optimal experimental designs are those where the researcher can exercise total control over the treatment levels to maximize a chosen mathematical property. As is common in literature, the experimental design is represented as a matrix where each column represents a variable, and each row represents a trial. We define a function that takes as input the design matrix and outputs its score. We then algorithmically adjust each entry until a design is found that minimizes or maximizes the function of interest.

In this thesis we study how to best minimize a prediction-variance criteria called the G-criteria, which is the maximum scaled-prediction-variance (SPV) over the entire design-space. Researchers may choose to implement this type of optimal experimental design when they need make accurate predictions on untested regions of their design space. In this thesis we apply various algorithms to the G-optimal problem, identifying and scoring candidate G-optimal designs with a combination of novel and legacy algorithms. We find that combining a novel scoring method called Gloptipoly with the best-known searching method (particle swarm optimization) produces the best-known G-optimal designs to-date.



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Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.