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There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
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The thesis focuses on the development of statistical theory in experimental design with applications in global optimization. It consists of four parts. In the first part, a criterion of design efficiency, under model uncertainty, is studied with reference to possibly nonregular fractions of general factorials. The results are followed by a numerical study and the findings are compared with those based on other design criteria.
In the second part, optimal designs are identified using Bayesian methods. This work is linked with response surface methodology where the first step is to perform factor screening, followed by response surface exploration using different experiment plans. A Bayesian analysis approach is used that aims to achieve both goals using one experiment design. In addition we use a Bayesian design criterion, based on the priors for the analysis approach. This creates an integrated design and analysis framework. To distinguish between competing models, the HD criterion is used, which is based on the pairwise Hellinger distance between predictive densities.
Mixed-level fractional factorial designs are commonly used in practice but its aliasing relations have not been studied in full rigor. These designs take the form of a product array. Aliasing patterns of mixed level factorial designs are discussed in the third part.
In the fourth part, design of experiment ideas are used to introduce a new global optimization technique called SELC (Sequential Elimination of Level Combinations), which is motivated by genetic algorithms but finds the optimum faster. The two key features of the SELC algorithm, namely, forbidden array and weighted mutation, enhance the performance of the search procedure. Illustration is given with the optimization of three functions, one of which is from Shekel's family. A real example on compound optimization is also given.
