Abstract
Effect aliasing is an inevitable consequence of using fractional factorial designs. For Gaussian random field models, advocated in some Bayesian design and computer experiment literature, the impact of effect aliasing has not received adequate attention. In this dissertation, we establish a kind of linear model structure to define effects for a Gaussian random field, and study effect aliasing in Gaussian random field models under fractional factorial designs with qualitative and with quantitative factors individually. An aliasing severity index is proposed to assess the severity level of aliasing, for which the notion of priority order and model complexity is established. Some impacts of aliasing on parameter estimation, posterior variances of effects under a Bayesian framework, and prediction variance are addressed as well.