Timothy Waite

Minimax efficient random experimental design strategies with application to model-robust design for prediction

Fisher stressed the importance of randomizing an experiment via random permutation of the allocation of treatments to experimental units; in an industrial context this usually amounts to randomizing the run order of the design. In this talk we take the idea of experimental randomization much further by introducing flexible new random design strategies in which the design to be applied is chosen at random from a distribution of possible designs. We discuss the philosophical justification for doing so from a game-theoretic perspective and it is shown that the new strategies give stronger bounds on both the expectation and survivor function of the loss distribution. The consequences of this approach are explored in several problems, including global prediction from a linear model contaminated by a discrepancy function from an L2-class. In this problem the performance improvement is dramatic: the new approach gives bounded expected loss, in contrast to previous designs for which the expected loss was unbounded.