Sequential Statistical Procedures
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| Author | : G. Barrie Wetherill |
| Publisher | : Chapman & Hall |
| Total Pages | : 256 |
| Release | : 1975 |
| Genre | : Mathematics |
| ISBN | : |
The sequential probability ratin test; Sequential tests between three hypotheses; Extensions to the SPRT; Some applications of Cox's theorem; Some methods leading to closed boundaries; Decision theory; Sequential estimation; Sequential estimation of points on regression functions; Sequential estimation of points on quantal response curves; Double sampling; Selection procedures.
| Author | : Abraham Wald |
| Publisher | : Courier Corporation |
| Total Pages | : 228 |
| Release | : 2013-11-26 |
| Genre | : Mathematics |
| ISBN | : 0486783235 |
The first to solve the general problem of sequential tests of statistical hypotheses, the author of this text explains his revolutionary theory of the sequential probability ratio test and its applications. 1947 edition.
| Author | : Jay Bartroff |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 250 |
| Release | : 2012-12-12 |
| Genre | : Medical |
| ISBN | : 1461461146 |
Sequential Experimentation in Clinical Trials: Design and Analysis is developed from decades of work in research groups, statistical pedagogy, and workshop participation. Different parts of the book can be used for short courses on clinical trials, translational medical research, and sequential experimentation. The authors have successfully used the book to teach innovative clinical trial designs and statistical methods for Statistics Ph.D. students at Stanford University. There are additional online supplements for the book that include chapter-specific exercises and information. Sequential Experimentation in Clinical Trials: Design and Analysis covers the much broader subject of sequential experimentation that includes group sequential and adaptive designs of Phase II and III clinical trials, which have attracted much attention in the past three decades. In particular, the broad scope of design and analysis problems in sequential experimentation clearly requires a wide range of statistical methods and models from nonlinear regression analysis, experimental design, dynamic programming, survival analysis, resampling, and likelihood and Bayesian inference. The background material in these building blocks is summarized in Chapter 2 and Chapter 3 and certain sections in Chapter 6 and Chapter 7. Besides group sequential tests and adaptive designs, the book also introduces sequential change-point detection methods in Chapter 5 in connection with pharmacovigilance and public health surveillance. Together with dynamic programming and approximate dynamic programming in Chapter 3, the book therefore covers all basic topics for a graduate course in sequential analysis designs.
| Author | : David Siegmund |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2013-04-09 |
| Genre | : Mathematics |
| ISBN | : 1475718624 |
The modern theory of Sequential Analysis came into existence simultaneously in the United States and Great Britain in response to demands for more efficient sampling inspection procedures during World War II. The develop ments were admirably summarized by their principal architect, A. Wald, in his book Sequential Analysis (1947). In spite of the extraordinary accomplishments of this period, there remained some dissatisfaction with the sequential probability ratio test and Wald's analysis of it. (i) The open-ended continuation region with the concomitant possibility of taking an arbitrarily large number of observations seems intol erable in practice. (ii) Wald's elegant approximations based on "neglecting the excess" of the log likelihood ratio over the stopping boundaries are not especially accurate and do not allow one to study the effect oftaking observa tions in groups rather than one at a time. (iii) The beautiful optimality property of the sequential probability ratio test applies only to the artificial problem of testing a simple hypothesis against a simple alternative. In response to these issues and to new motivation from the direction of controlled clinical trials numerous modifications of the sequential probability ratio test were proposed and their properties studied-often by simulation or lengthy numerical computation. (A notable exception is Anderson, 1960; see III.7.) In the past decade it has become possible to give a more complete theoretical analysis of many of the proposals and hence to understand them better.
| Author | : Samuel Kotz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 576 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461206677 |
Volume III includes more selections of articles that have initiated fundamental changes in statistical methodology. It contains articles published before 1980 that were overlooked in the previous two volumes plus articles from the 1980's - all of them chosen after consulting many of today's leading statisticians.
| Author | : Alexander Tartakovsky |
| Publisher | : CRC Press |
| Total Pages | : 600 |
| Release | : 2014-08-27 |
| Genre | : Mathematics |
| ISBN | : 1439838216 |
Sequential Analysis: Hypothesis Testing and Changepoint Detection systematically develops the theory of sequential hypothesis testing and quickest changepoint detection. It also describes important applications in which theoretical results can be used efficiently. The book reviews recent accomplishments in hypothesis testing and changepoint detecti
| Author | : Christopher Jennison |
| Publisher | : CRC Press |
| Total Pages | : 416 |
| Release | : 1999-09-15 |
| Genre | : Mathematics |
| ISBN | : 9781584888581 |
Group sequential methods answer the needs of clinical trial monitoring committees who must assess the data available at an interim analysis. These interim results may provide grounds for terminating the study-effectively reducing costs-or may benefit the general patient population by allowing early dissemination of its findings. Group sequential methods provide a means to balance the ethical and financial advantages of stopping a study early against the risk of an incorrect conclusion. Group Sequential Methods with Applications to Clinical Trials describes group sequential stopping rules designed to reduce average study length and control Type I and II error probabilities. The authors present one-sided and two-sided tests, introduce several families of group sequential tests, and explain how to choose the most appropriate test and interim analysis schedule. Their topics include placebo-controlled randomized trials, bio-equivalence testing, crossover and longitudinal studies, and linear and generalized linear models. Research in group sequential analysis has progressed rapidly over the past 20 years. Group Sequential Methods with Applications to Clinical Trials surveys and extends current methods for planning and conducting interim analyses. It provides straightforward descriptions of group sequential hypothesis tests in a form suited for direct application to a wide variety of clinical trials. Medical statisticians engaged in any investigations planned with interim analyses will find this book a useful and important tool.
| Author | : Z. Govindarajulu |
| Publisher | : Academic Press |
| Total Pages | : 585 |
| Release | : 2014-06-20 |
| Genre | : Mathematics |
| ISBN | : 1483263320 |
Probability and Mathematical Statistics, Volume 26: Sequential Statistical Procedures provides information pertinent to the sequential procedures that are concerned with statistical analysis of data. This book discusses the fundamental aspects of sequential estimation. Organized into four chapters, this volume begins with an overview of the essential feature of sequential procedure. This text then examines the sequential probability ratio test procedure and provides a method of constructing a most powerful test for a simple hypothesis versus simple alternative-testing problem. Other chapters consider the problem of testing a composite hypothesis against a composite alternative. This book discusses as well the theory of sequential tests that is appropriate for distinguishing between two simple or composite hypotheses. The final chapter deals with the theory of sequential estimation. This book is a valuable resource for graduate students, research workers, and users of sequential procedures.
| Author | : Bhaskar Kumar Ghosh |
| Publisher | : |
| Total Pages | : 472 |
| Release | : 1970 |
| Genre | : Sequences (Mathematics) |
| ISBN | : |
The purpose of this book is to give a systematic account of the mathematical theory in this field as applied to problems of hypothesis testing. The resulting methods are predominantly sequential probability ratio tests. A brief account of classical tests under the neyman-pearson formulation is included. The notion of sequential analysis has been used in some form or other in various branches of statistical inference. We may classify these branches into three broad categories: Statistical tests of hypotheses, statistical estimation, and statistical decision theory.
| Author | : Roger Bakeman |
| Publisher | : Cambridge University Press |
| Total Pages | : 226 |
| Release | : 1997-03-13 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9780521574273 |
Mothers and infants exchanging gleeful vocalizations, married couples discussing their problems, children playing, birds courting and monkeys fighting have this in common: their interactions with others unfold over time. Almost anyone who is interested can observe and describe such phenomena. But usually scientists demand more. They want observations that are replicable and amenable to scientific analysis, while still faithful to the dynamics of the phenomena studied. This book provides a straightforward introduction to scientific methods for observing social behavior. Because of the importance of time in the dynamics of social interaction, sequential approaches to analyzing and understanding social behavior are emphasized. An advanced knowledge of statistical analysis is not required. Instead, the authors present fundamental concepts and offer practical advice.
