DOI
https://doi.org/10.25772/6QS3-E016
Defense Date
2010
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
First Advisor
David Edwards
Abstract
The path of steepest ascent can used to optimize a response in an experiment, but problems can occur with multiple responses. Past approaches to this issue such as Del Castillo’s overlap of confidence cones and Mee and Xiao’s Pareto Optimality, have not considered the correlations of the responses or parameter uncertainty. We propose a new method using the Bayesian reliability to calculate this direction. We utilize this method with four examples: a 2 factor, 2-response experiment where the paths of steepest ascent are similar, ensuring our results match Del Castillo’s and Mee and Xiao’s; a 2 factor, 2-response experiment with disparate paths of steepest ascent illustrating the importance of the Bayesian reliability; two simulation examples, showing parameter uncertainty is considered; and a 5 factor, 2-response experiment proving this method is not dimensional limited. With a Bayesian reliable point, a direction in multivariate steepest ascent can be found.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
May 2010