Data-driven Kriging models based on FANOVA-decomposition

The situation of time consuming computer experiments is considered, where the output is deterministic and the data generating function is of high complexity. In such situations the underlying functions often are non additive but at the same time, not all interactions are active. Hence neither a model considering all interactions as well as an additive model is adequate. As a solution a modified Kriging model is proposed, which reflects the interaction structure inherent to the data generating mechanism. This is achieved by exploring the interaction structure of the output based on FANOVA methods. For illustrating the interaction structure, a graph is developed which summaries the structure of the output generating function in additive parts. Finally, modified covariance kernels are defined, which allow for a more precise modeling of simulation output.