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Field name	Details
Dewey Class	519.2
Title	Optimal Sequentially Planned Decision Procedures ([EBook] /) / edited by Norbert Schmitz.
Added Personal Name	Schmitz, Norbert editor.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer New York, , 1993.
Physical Details	XII, 207 p. : online resource.
Series	Lecture Notes in Statistics 0930-0325 ; ; 79
ISBN	9781461227366
Summary Note	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 (1.8» 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. Bayes optimality, minimax-properties, "uniform" optimality with respect to expected sample sizes - gave rise to the development of a general statistical decision theory. As a conse quence, the SPRT's played a dominating role in the further development of sequential analysis and, more generally, in theoretical statistics.:
Contents note	I. Introduction -- § 1 Sequential statistical procedures -- § 2 Objectives of sequential analysis -- § 3 Historical remarks on the development of sequential analysis -- § 4 Examples of sequential procedures; purely sequential statistical decision procedures -- § 5 Objections to purely sequential statistical decision procedures -- § 6 Sequentially planned statistical procedures -- II. Optimal sequential sampling plans -- § 1 Problems of optimal sampling -- § 2 Optimal sampling plans for finite horizon -- § 3 Existence of optimal sampling plans for general A -- § 4 Optimal sampling plans for the Markov case -- III. Sequentially planned tests; sequentially planned probability ratio tests -- § 1 Notation -- § 2 The iid case -- § 3 Sequentially planned probability ratio tests -- § 4 Algorithms for computing the OC- and ASC-function of SPPRT’s in the iid case -- § 5 Remarks on the implementation of the algorithms; Examples -- § 6 Remarks on the comparison of the methods and on convergence-improvements for the BF-/EV- method -- IV. Bayes-optimal sequentially planned decision procedures -- § 1 Introduction -- § 2 Bayes-procedures -- § 3 A posteriori-distributions -- § 4 Bayes-optimal sampling plans; Markov case -- V. Optimal sequentially planned tests under side conditions -- § 1 Decision problems with side conditions -- § 2 Characterizations of optimal sequentially planned decision procedures -- § 3 Sequentially planned tests for simple hypotheses in the iid case -- § 4 The modified Kiefer-Weiss problem in the iid case -- § 5 Locally optimal sequentially planned tests in the dominated iid case -- § 6 Remarks on the monotonicity of the power functions of SPPRT’s and GSPPRT’s -- Appendix A: Mathematical models for sequentially planned sampling procedures -- § A.1 The concept of policies by Mandelbaum and Vanderbei -- § A.2 The concept of tactics by Krengel and Sucheston -- § A.3 The concept of decision functions by Washburn and Willsky -- § A.4 The concept of stopped decision models by Rieder -- Appendix B: Implementation of the algorithms EV, BF and ILE; Diophantine Approximation -- § B.1 Listing of the modules -- § B.2 Diophantine approximation -- Appendix C: References, Bibliography.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-2736-6
Links to Related Works	Subject References: Mathematics . Probabilities . Probability theory and stochastic processes . Authors: Schmitz, Norbert . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Statistics . Classification: 519.2 .

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Optimal Sequentially Planned Decision Procedures

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