Change-point Problems


Book Description







Sequential Analysis


Book Description

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 detection both in decision-theoretic (Bayesian) and non-decision-theoretic (non-Bayesian) contexts. The authors not only emphasize traditional binary hypotheses but also substantially more difficult multiple decision problems. They address scenarios with simple hypotheses and more realistic cases of two and finitely many composite hypotheses. The book primarily focuses on practical discrete-time models, with certain continuous-time models also examined when general results can be obtained very similarly in both cases. It treats both conventional i.i.d. and general non-i.i.d. stochastic models in detail, including Markov, hidden Markov, state-space, regression, and autoregression models. Rigorous proofs are given for the most important results. Written by leading authorities in the field, this book covers the theoretical developments and applications of sequential hypothesis testing and sequential quickest changepoint detection in a wide range of engineering and environmental domains. It explains how the theoretical aspects influence the hypothesis testing and changepoint detection problems as well as the design of algorithms.




Nonparametric Methods in Change Point Problems


Book Description

The explosive development of information science and technology puts in new problems involving statistical data analysis. These problems result from higher re quirements concerning the reliability of statistical decisions, the accuracy of math ematical models and the quality of control in complex systems. A new aspect of statistical analysis has emerged, closely connected with one of the basic questions of cynergetics: how to "compress" large volumes of experimental data in order to extract the most valuable information from data observed. De tection of large "homogeneous" segments of data enables one to identify "hidden" regularities in an object's behavior, to create mathematical models for each seg ment of homogeneity, to choose an appropriate control, etc. Statistical methods dealing with the detection of changes in the characteristics of random processes can be of great use in all these problems. These methods have accompanied the rapid growth in data beginning from the middle of our century. According to a tradition of more than thirty years, we call this sphere of statistical analysis the "theory of change-point detection. " During the last fifteen years, we have witnessed many exciting developments in the theory of change-point detection. New promising directions of research have emerged, and traditional trends have flourished anew. Despite this, most of the results are widely scattered in the literature and few monographs exist. A real need has arisen for up-to-date books which present an account of important current research trends, one of which is the theory of non parametric change--point detection.




Parametric Statistical Change Point Analysis


Book Description

This revised and expanded second edition is an in-depth study of the change point problem from a general point of view, as well as a further examination of change point analysis of the most commonly used statistical models. Change point problems are encountered in such disciplines as economics, finance, medicine, psychology, signal processing, and geology, to mention only several. More recently, change point analysis has been found in extensive applications related to analyzing biomedical imaging data and gene expression data. Extensive examples throughout the text emphasize key concepts and different methodologies used. New examples of change point analysis in modern molecular biology and other fields such as finance and air traffic control have been added to this second edition.




Applied Data Analytic Techniques For Turning Points Research


Book Description

This innovative volume demonstrates the use of a range of statistical approaches that examine "turning points" (a change in direction, magnitude, or meaning) in real data. Analytic techniques are illustrated with real longitudinal data from a variety of fields. As such the book will appeal to a variety of researchers including: Developmental researchers interested in identifying factors precipitating turning points at various life stages. Medical or substance abuse researchers looking for turning points in disease or recovery. Social researchers interested in estimating the effects of life experiences on subsequent behavioral changes. Interpersonal behavior researchers looking to identify turning points in relationships. Brain researchers needing to discriminate the onset of an experimentally produced process in a participant. The book opens with the goals and theoretical considerations in defining turning points. An overview of the methods presented in subsequent chapters is then provided. Chapter goals include discriminating "local" from long-term effects, identifying variables altering the connection between trajectories at different life stages, locating non-normative turning points, coping with practical distributional problems in trajectory analyses, and changes in the meaning and connections between variables in the transition to adulthood. From an applied perspective, the book explores such topics as antisocial/aggressive trajectories at different life stages, the impact of imprisonment on criminal behavior, family contact trajectories in the transition to adulthood, sustained effects of substance abuse, alternative models of bereavement, and identifying brain changes associated with the onset of a new brain process. Ideal for advanced students and researchers interested in identifying significant change in data in a variety of fields including psychology, medicine, education, political science, criminology, and sociology.




Applied Statistics


Book Description

Series C (Applied Statistics) of the Journal of the Royal Statistical Society was founded in 1952. It promotes papers that are driven by real life problems and that make a novel contribution to the subject.




Limit Theorems in Change-Point Analysis


Book Description

Change-point problems arise in a variety of experimental and mathematical sciences, as well as in engineering and health sciences. This rigorously researched text provides a comprehensive review of recent probabilistic methods for detecting various types of possible changes in the distribution of chronologically ordered observations. Further developing the already well-established theory of weighted approximations and weak convergence, the authors provide a thorough survey of parametric and non-parametric methods, regression and time series models together with sequential methods. All but the most basic models are carefully developed with detailed proofs, and illustrated by using a number of data sets. Contains a thorough survey of: The Likelihood Approach Non-Parametric Methods Linear Models Dependent Observations This book is undoubtedly of interest to all probabilists and statisticians, experimental and health scientists, engineers, and essential for those working on quality control and surveillance problems. Foreword by David Kendall




Change-point Problems


Book Description

This e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press.




Change-Point Analysis in Nonstationary Stochastic Models


Book Description

This book covers the development of methods for detection and estimation of changes in complex systems. These systems are generally described by nonstationary stochastic models, which comprise both static and dynamic regimes, linear and nonlinear dynamics, and constant and time-variant structures of such systems. It covers both retrospective and sequential problems, particularly theoretical methods of optimal detection. Such methods are constructed and their characteristics are analyzed both theoretically and experimentally. Suitable for researchers working in change-point analysis and stochastic modelling, the book includes theoretical details combined with computer simulations and practical applications. Its rigorous approach will be appreciated by those looking to delve into the details of the methods, as well as those looking to apply them.