A sequential maximum projection design framework for computer experiments with inert factors

Many computer experiments involve a large number of input factors, but many of them are inert and only a subset are important. This paper develops a new sequential design framework that can accommodate multiple responses and quickly screen out inert factors so that the final design is space-filling with respect to the active factors. By folding over Latin hypercube designs with sliced structure, this sequential design can have flexible sample size in each stage and also ensure that each stage, as well as the whole combined design, are all approximately Latin hypercube designs. The sequential framework does not require prescribing the total sample size and, under the presence of inert factors, can lead to substantial savings in simulation resources. Even if all factors are important, the proposed sequential design can still achieve a similar overall space-filling property compared to a maximin Latin hypercube design optimized in a single stage.