Abstract: | Optimality properties of approximate block designs are studied under variations of (1) the class of competing designs, (2) the optimality criterion, (3) the parametric function of interest, and (4) the statistical model. The designs which are optimal turn out to be the product of their treatment and block marginals, and uniform designs when the support is specified in advance. Optimality here means uniform, universal, and simultaneous jp-optimality. The classical balanced incomplete block designs are embedded into this approach, and shown to be simultaneously jp-optimal for a maximal system of identifiable parameters. A geometric account of universal optimality is given which applies beyond the context of block designs. |