Ebook: Optimal Sequentially Planned Decision Procedures

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.

---

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.

---

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.
Content:
Front Matter....Pages N1-x
Introduction....Pages 1-28
Optimal sequential sampling plans....Pages 29-57
Sequentially planned tests; sequentially planned probability ratio tests....Pages 58-104
Bayes-optimal sequentially planned decision procedures....Pages 105-126
Optimal sequentially planned tests under side conditions....Pages 127-163
Back Matter....Pages 164-213

---

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.
Content:
Front Matter....Pages N1-x
Introduction....Pages 1-28
Optimal sequential sampling plans....Pages 29-57
Sequentially planned tests; sequentially planned probability ratio tests....Pages 58-104
Bayes-optimal sequentially planned decision procedures....Pages 105-126
Optimal sequentially planned tests under side conditions....Pages 127-163
Back Matter....Pages 164-213
....