JSM 2004 - Toronto

Abstract #302094

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Activity Number: 230
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #302094
Title: Optimal Sequential Planning Techniques
Author(s): Claudia Schmegner*+ and Michael Baron
Companies: DePaul University and University of Texas, Dallas
Address: Mathematics Department, Chicago, IL, 60614,
Keywords: sequential procedures ; cost function ; Bayes stopping time ; sequentially planned probability ratio test ; sufficiency ; randomization
Abstract:

Sequential planning extends and generalizes the classical sequential schemes. Observations are sampled in groups of variable sizes, rather than one by one. A sampling strategy, in terms of batch sizes and the number of batches, is determined sequentially. We discuss optimality of sequential plans under a suitable risk function that, besides the total cost of collecting the observations, includes a new term consisting of the costs for each sampled batch. It is shown that only nonrandomized sequential plans based on a sufficient statistic have to be considered in order to achieve Bayes optimality. Sequential planning on a lattice is considered in detail, and methods of risk evaluation and comparison are derived.

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