In Computing Science and Statistics 27, (1995).

Determining Optimal Few-Stage Allocation Procedures

Janis Hardwick
Statistics Department, University of Michigan

Quentin F. Stout
EECS Department, University of Michigan

Abstract: This paper gives flexible algorithms for the design of optimal experiments involving Bernoulli populations in which allocation is done in stages. It is assumed that the outcomes of the previous stage are available before the allocations for the next stage are decided and that the total sample size for the experiment is fixed. At each stage, one must decide how many observations to take and how many to sample from each of two alternative populations. Of particular interest are 2- and 3-stage experiments.

The algorithms can be used to optimize experiments of useful sample sizes. They are quite flexible and can be used with arbitrary objective functions. To illustrate their use, and the types of behavior that one encounters, they are applied here to two estimation problems. Results indicate that, for problems of moderate size, published asymptotic analyses do not always represent the true behavior of the optimal stage sizes, and that initial stages should be much larger than previously believed. This information suggests that one might approach large problems by extrapolating optimal solutions for moderate sample sizes; and, that approaches of this sort could give design guidelines that are far more explicit (and hopefully more accurate) than those obtained through asymptotic analyses alone.

Keywords: sequential allocation, selection, estimation, dynamic programming, Bayesian

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