Bayesian Lasso with Effect Heredity Principle

Abstract

The Bayesian Lasso is a variable selection method that can be applied in situations where there are more variables than observations; thus, both main effects and interaction effects can be considered in screening experiments. To apply the Bayesian framework to experiments involving the effect heredity principle, which governs the relationships between interactions and their corresponding main effects, several initial tunings of the Bayesian framework are required. However, it is rather unnatural to specify these tuning values before running an experiment. In this paper, we propose models that do not require the initial tuning values to be specified in advance. The proposed methods are demonstrated with screening examples such as Plackett-Burman and mixed-level design.

Lasso for hierarchical polynomial models

“…Finally, the authors in [6] explored a general model parametrization that guarantees hierarchy, but in the face of nonlinearity of this approach, they developed hierarchy in a Bayesian context. Another proposal within the context of Bayesian analysis is [18].…”