Some Criterion-based Experimental Designs

In Chapter 5, we considered designs that attempt to spread observations evenly throughout the experimental region. We called such designs space-filling designs. One rationale for using a space-filling design is the following. If we believe interesting features of the true model are just as likely to be in one part of the experimental region as another, we should take observations in all portions of the experimental region. A space-filling design attempts to do this. One difficulty is deciding exactly what it means for a set of observations to be evenly spread throughout the experimental region. There are many ways in which a design might be considered space-filling, and we discussed several in Chapter 5. Which design is best is not clear.