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Optimal Sequentially Planned Decision Procedures

By: Norbert Schmitz, G. Duscha, J. LÃ¼bbert

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This volume is concerned with statistical procedures where the data are collected in sequentially designed groups. The basic premise here is that the expected total sample size is not always the appropriate criterion for evaluating statistical procedures, especially for nonlinear sampling costs (e.g. additive fixed costs) and in clinical trials. In fact, this criterion seems to have been a hindrance to the practical use of Wald's sequential probability ratio test (SPRT) despite its well-known optimum properties. This volume systematically develops decision procedures which retain the possibility of early stopping and remove some of the disadvantages of one-at-a-time sampling. In particular, for generalizations of the SPRT algorithms, methods for computing characteristics (such as operating characteristics or power functions, expected sampling costs, etc.) are developed and implemented. The procedures turn out to be optimal in a Bayesian sense as well as for problems with side conditions (e.g. specified bounds on error probabilities or expected sampling costs). A theory of optimal sampling is developed in order to prove the various properties of the procedures.

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Non-Fiction Mathematics Probability & Statistics Reference, Information & Interdisciplinary Subjects Research & Information Decision Theory Applied Mathematics Stochastics

Preface
Introduction	p. 1
Optimal sequential sampling plans	p. 29
Sequentially planned tests; sequentially planned probability ratio tests	p. 58
Bayes-optimal sequentially planned decision procedures	p. 105
Optimal sequentially planned tests under side conditions	p. 127
Appendix A: Mathematical models for sequentially planned sampling procedures	p. 164
Appendix B: Implementation of the algorithms EV, BF and ILE; Diophantine Approximation	p. 178
Appendix C: References, Bibliography	p. 199
Subject Index	p. 206
Table of Contents provided by Blackwell. All Rights Reserved.

Optimal Sequentially Planned Decision Procedures

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