Optimal Sequentially Planned Decision Procedures PDF Download

Author: Norbert Schmitz
Publisher: Springer Science & Business Media
ISBN: 1461227364
Category : Mathematics
Languages : en
Pages : 222

View

Book Description
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.

Author: Morris H. DeGroot
Publisher: John Wiley & Sons
ISBN: 9780471680291
Category : Mathematics
Languages : en
Pages : 514

View

Book Description
The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.

Author: Brian McCall
Publisher: Routledge
ISBN: 1134422342
Category : Business & Economics
Languages : en
Pages : 674

View

Book Description
The economics of search is a prominent component of economic theory, and it has a richness and elegance that underpins a host of practical applications. In this book Brian and John McCall present a comprehensive overview of the economic theory of search, from the classical model of job search formulated 40 years ago to the recent developments in eq

Author: Nitis Mukhopadhyay
Publisher: CRC Press
ISBN: 1420010026
Category : Mathematics
Languages : en
Pages : 512

View

Book Description
Interactively Run Simulations and Experiment with Real or Simulated Data to Make Sequential Analysis Come AliveTaking an accessible, nonmathematical approach to this field, Sequential Methods and Their Applications illustrates the efficiency of sequential methodologies when dealing with contemporary statistical challenges in many areas.The book fir

Author: Annpey Pong
Publisher: CRC Press
ISBN: 1439810176
Category : Mathematics
Languages : en
Pages : 475

View

Book Description
In response to the US FDA's Critical Path Initiative, innovative adaptive designs are being used more and more in clinical trials due to their flexibility and efficiency, especially during early phase development. Handbook of Adaptive Designs in Pharmaceutical and Clinical Development provides a comprehensive and unified presentation of the princip

Author: Shelemyahu Zacks
Publisher: John Wiley & Sons
ISBN: 0470466944
Category : Medical
Languages : en
Pages : 411

View

Book Description
An expert introduction to stage-wise adaptive designs in all areas of statistics Stage-Wise Adaptive Designs presents the theory and methodology of stage-wise adaptive design across various areas of study within the field of statistics, from sampling surveys and time series analysis to generalized linear models and decision theory. Providing the necessary background material along with illustrative S-PLUS functions, this book serves as a valuable introduction to the problems of adaptive designs. The author begins with a cohesive introduction to the subject and goes on to concentrate on generalized linear models, followed by stage-wise sampling procedures in sampling surveys. Adaptive forecasting in the area of time series analysis is presented in detail, and two chapters are devoted to applications in clinical trials. Bandits problems are also given a thorough treatment along with sequential detection of change-points, sequential applications in industrial statistics, and software reliability. S-Plus functions are available to accompany particular computations, and all examples can be worked out using R, which is available on the book's related FTP site. In addition, a detailed appendix outlines the use of these software functions, while an extensive bibliography directs readers to further research on the subject matter. Assuming only a basic background in statistical topics, Stage-Wise Adaptive Designs is an excellent supplement to statistics courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and practitioners in the fields of statistics and biostatistics.

Author: Gernot Wassmer
Publisher: Springer
ISBN: 3319325620
Category : Medical
Languages : en
Pages : 310

View

Book Description
This book provides an up-to-date review of the general principles of and techniques for confirmatory adaptive designs. Confirmatory adaptive designs are a generalization of group sequential designs. With these designs, interim analyses are performed in order to stop the trial prematurely under control of the Type I error rate. In adaptive designs, it is also permissible to perform a data-driven change of relevant aspects of the study design at interim stages. This includes, for example, a sample-size reassessment, a treatment-arm selection or a selection of a pre-specified sub-population. Essentially, this adaptive methodology was introduced in the 1990s. Since then, it has become popular and the object of intense discussion and still represents a rapidly growing field of statistical research. This book describes adaptive design methodology at an elementary level, while also considering designing and planning issues as well as methods for analyzing an adaptively planned trial. This includes estimation methods and methods for the determination of an overall p-value. Part I of the book provides the group sequential methods that are necessary for understanding and applying the adaptive design methodology supplied in Parts II and III of the book. The book contains many examples that illustrate use of the methods for practical application. The book is primarily written for applied statisticians from academia and industry who are interested in confirmatory adaptive designs. It is assumed that readers are familiar with the basic principles of descriptive statistics, parameter estimation and statistical testing. This book will also be suitable for an advanced statistical course for applied statisticians or clinicians with a sound statistical background.

Author: Ibrahim Rahimov
Publisher: Springer Science & Business Media
ISBN: 1461242169
Category : Mathematics
Languages : en
Pages : 207

View

Book Description
The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.

Author: C.C. Heyde
Publisher: Springer Science & Business Media
ISBN: 1461225582
Category : Mathematics
Languages : en
Pages : 189

View

Book Description
This volume presents the edited proceedings of the First World Congress on Branching Processes. The contributions present new research and surveys of the current research activity in this field. As a result, all those undertaking research in the subject will find this a timely and high-quality volume to have on their shelves.

Author: Denis Bosq
Publisher: Springer Science & Business Media
ISBN: 146840489X
Category : Mathematics
Languages : en
Pages : 181

View

Book Description
This book provides a mathematically rigorous treatment of the theory of nonparametric estimation and prediction for stochastic processes. It discusses discrete time and continuous time, and the emphasis is on the kernel methods. Several new results are presented concerning optimal and superoptimal convergence rates. How to implement the method is discussed in detail and several numerical results are presented. This book will be of interest to specialists in mathematical statistics and to those who wish to apply these methods to practical problems involving time series analysis.