ABSTRACT
This chapter is about adaptive allocation rules which depend on the past history of
the experiment only through the sequence of previous treatment assignments. They
have the advantage that the whole experiment can be designed in advance, before
collecting the responses, and inference may be conditional on the design. Sequential
procedureswhere the choice of the next design point is made on the basis of the previ-
ous points are, for instance, the Wynn−Fedorov designs for the linear model (Wynn, 1972; Fedorov, 1972), which at each step add design points where the variance of
the predicted response is highest so as to converge to D-optimality. For instance in the case of a homoscedastic linear model for estimating v treatments, at each step the Wynn−Fedorov algorithm would choose to observe the under-represented treatment, with no preference in case of a tie. However, the Wynn−Fedorov designs are deterministic, whereas in this book we are concerned with randomized assignments.
