Interactions and computer experiments

Identifying interactions and understanding the underlying generating mechanism is essential for interpreting the response of black-box models. We offer a systematic analysis of interaction types and corresponding sources, merging results of the broad statistical literature with findings developed within the computer experiment literature. Piecewise-definiteness emerges a self-standing interaction mechanism, alternative to the presence of interaction terms. We find that the scale of the analysis is essential for interpretation, and that no single method is capable of providing the correct identification of the underlying interaction generating mechanisms; conversely a combined approach involving indicators at difference scales is required. We propose a graphical tool called Mikado plot that exploits the link between interaction indicators at the finite scale and global scales to ease the regional visualization of two-factor interactions. The findings are illustrated via numerical experiments with three well-known computer models of different dimensionality and structure.