Towards a Unified Theory to the Selection of Factorial Designs

Abstract

Factorial designs are quite common in scientific and industrial investigations. Given a treatment structure and a block structure in an experiment, the selection of efficient factorial designs is crucial to extract valuable information from the underlying system. Most relevant research in the literature was built on case-by-case bases such as block designs, split-plot designs, and strip-plot designs. In this talk, I will introduce a unified theory for selecting optimal factorial designs under complicated treatment structures and block structures, including multi-stratum designs and multi-platform online designs. Additionally, this theory enables experimenters to derive their own optimality criteria for design selection. ??? Keywords: block structure, mixed-effect model, stratum variance, Gaussian functional prior, minimum aberration.