Adaptive Design for Contour Estimation from Computer Experiments with Quantitative and Qualitative Inputs

Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments. This paper proposes an adaptive design approach for estimating a contour from computer experiments with quantitative and qualitative inputs. A new criterion is introduced to search for the follow-up inputs. The key features of the proposed criterion are (a) the criterion yields adaptive search regions; and (b) it is region-based cooperative in that for each stage of the sequential procedure, the candidate points in the design space is divided into two disjoint groups using confidence bounds, and within each group, an acquisition function is used to select a candidate point. Among the two selected points, a point that is closer to the contour level with the higher uncertainty or that has higher uncertainty when the distance between its prediction and the contour level is within a threshold is chosen. The proposed approach provides empirically more accurate contour estimation than existing approaches as illustrated in numerical examples and a real application. Theoretical justification of the proposed adaptive search region is given.