Functionally Induced Priors for the Analysis of Experiments

This work develops the idea of using functional priors for the design and analysis of three-level and higher-level experiments. Developing a prior distribution for model parameters is challenging, because a factor can be qualitative or quantitative. We propose appropriate correlation functions and coding schemes so that the prior distribution is simple and the results are interpretable. The prior incorporates well-known principles, such as effect hierarchy and effect heredity, which helps resolve the aliasing problems in fractional designs almost automatically. The usefulness of the new approach is illustrated through the analysis of some real experiments.