5 Adaptive designs for parametric models

Publisher Summary This chapter discusses several adaptive designs for parametric models. These models specify the families of distributions of the observed random variables at the various design levels. Adaptive designs are those performed in stages (sequentially) to correct in each stage the design level and approach the optimal level(s) as the number of stages grow. Adaptive designs are needed when the optimal design level(s) depend on some unknown parameter(s) or distributions. The chapter also discusses the important problem of optimal allocation of experiments along with a sequential estimation problem, in which two alternative experiments are available and the objective is to minimize the expected total number of trials. The problems of optimal allocation are also known as “bandit problems.” Allocation problems are one type of adaptive designs in which sequential stopping rules play an important role. Such problems can be solved by a non-parametric methodology known as “stochastic approximation.”