Replication in random translation designs

Replication is a commonly recommended feature of experimental designs. However, its impact in model-robust design is relatively under-explored; indeed, replication is impossible within the current formulation of random translation designs, which were introduced recently for model-robust prediction. Here we extend the framework of random translation designs to allow replication, and quantify the resulting performance impact. The extension permits a simplification of our earlier heuristic for constructing random translation strategies from a traditional $V$-optimal design. Namely, in the previous formulation any replicates of the $V$-optimal design first had to be split up before a random translation can be applied to the design points. With the new framework we can instead preserve the replicates instead if we so wish. Surprisingly, we find that in low-dimensional problems it is often substantially more efficient to continue to split replicates, while in high-dimensional problems it can be substantially better to retain replicates.