Aliasing in Gaussian Random Field Regression Models for Qualitative Factors

Abstract

Effect aliasing is an inevitable consequence of using fractional factorial designs. For Gaussian random field regression models, advocated in some Bayesian design and computer experiment literature, the impact of effect aliasing has not received adequate attention. In the article, we establish a kind of linear model structure to define effects for a Gaussian random field, and study effect aliasing in Gaussian random field regression models with qualitative factors. The importance evaluation of the effects for a Gaussian random field is developed. Under regular fractional factorial designs, the aliasing pattern for the effects in a Gaussian random field is shown to be the same as that for fixed factorial effects but the aliasing severity can be different. An aliasing severity index is proposed to assess the severity level of aliasing and a statistical rationale is provided. Key words: Fractional factorials, Bayesian design, computer experiments, kriging.