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TitleOptimal Sequentially Planned Decision Procedures [electronic resource] / edited by Norbert Schmitz
ImprintNew York, NY : Springer New York, 1993
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Descript XII, 207 p. online resource


Learning from experience, making decisions on the basis of the available information, and proceeding step by step to a desired goal are fundamental behavioural qualities of human beings. Nevertheless, it was not until the early 1940's that such a statistical theory - namely Sequential Analysis - was created, which allows us to investigate this kind of behaviour in a precise manner. A. Wald's famous sequential probability ratio test (SPRT; see example (1.8ยป turned out to have an enormous influence on the development of this theory. On the one hand, Wald's fundamental monograph "Sequential Analysis" ([Wa]*) is essentially centered around this test. On the other hand, important properties of the SPRT - e.g. Bayesยญ optimality, minimax-properties, "uniform" optimality with respect to expected sample sizes - gave rise to the development of a general statistical decision theory. As a conseยญ quence, the SPRT's played a dominating role in the further development of sequential analysis and, more generally, in theoretical statistics


I. Introduction -- ยง 1 Sequential statistical procedures -- ยง 2 Objectives of sequential analysis -- ยง 3 Historical remarks on the development of sequential analysis -- ยง 4 Examples of sequential procedures; purely sequential statistical decision procedures -- ยง 5 Objections to purely sequential statistical decision procedures -- ยง 6 Sequentially planned statistical procedures -- II. Optimal sequential sampling plans -- ยง 1 Problems of optimal sampling -- ยง 2 Optimal sampling plans for finite horizon -- ยง 3 Existence of optimal sampling plans for general A -- ยง 4 Optimal sampling plans for the Markov case -- III. Sequentially planned tests; sequentially planned probability ratio tests -- ยง 1 Notation -- ยง 2 The iid case -- ยง 3 Sequentially planned probability ratio tests -- ยง 4 Algorithms for computing the OC- and ASC-function of SPPRTโ{128}{153}s in the iid case -- ยง 5 Remarks on the implementation of the algorithms; Examples -- ยง 6 Remarks on the comparison of the methods and on convergence-improvements for the BF-/EV- method -- IV. Bayes-optimal sequentially planned decision procedures -- ยง 1 Introduction -- ยง 2 Bayes-procedures -- ยง 3 A posteriori-distributions -- ยง 4 Bayes-optimal sampling plans; Markov case -- V. Optimal sequentially planned tests under side conditions -- ยง 1 Decision problems with side conditions -- ยง 2 Characterizations of optimal sequentially planned decision procedures -- ยง 3 Sequentially planned tests for simple hypotheses in the iid case -- ยง 4 The modified Kiefer-Weiss problem in the iid case -- ยง 5 Locally optimal sequentially planned tests in the dominated iid case -- ยง 6 Remarks on the monotonicity of the power functions of SPPRTโ{128}{153}s and GSPPRTโ{128}{153}s -- Appendix A: Mathematical models for sequentially planned sampling procedures -- ยง A.1 The concept of policies by Mandelbaum and Vanderbei -- ยง A.2 The concept of tactics by Krengel and Sucheston -- ยง A.3 The concept of decision functions by Washburn and Willsky -- ยง A.4 The concept of stopped decision models by Rieder -- Appendix B: Implementation of the algorithms EV, BF and ILE; Diophantine Approximation -- ยง B.1 Listing of the modules -- ยง B.2 Diophantine approximation -- Appendix C: References, Bibliography

Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes


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