**Determining Optimal Few-Stage Allocation Procedures**

Janis Hardwick

Statistics Department, University of Michigan

Quentin F. Stout

EECS Department, University of Michigan

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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