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2012 | Buch

Parametric Statistical Change Point Analysis

With Applications to Genetics, Medicine, and Finance

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Über dieses Buch

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, array Comparative Genomic Hybridization (aCGH) data, and gene expression data.

The exposition throughout the work is clear and systematic, with a great deal of introductory material included. Different models are presented in each chapter, including gamma and exponential models, rarely examined thus far in the literature. Extensive examples throughout the text emphasize key concepts and different methodologies used, namely the likelihood ratio criterion as well as the Bayesian and information criterion approaches. New examples of change point analysis in modern molecular biology and other fields such as finance and air traffic control are added in this second edition. Also included are two new chapters on change points in the hazard function and other practical change point models such as the epidemic change point model and a smooth-and-abrupt change point model. An up-to-date comprehensive bibliography and two indices round out the work.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Preliminaries
Abstract
The world is filled with changes. An awareness of those changes can help people avoid unnecessary losses and to harness beneficial transitions. In many practical situations, a statistician is faced with the problem of detecting the number of change points or jumps and their locations. This is known as the change point problem. Enormous practical problems can be found in many disciplines.
Jie Chen, Arjun K. Gupta
Chapter 2. Univariate Normal Model
Abstract
Let x1, x2,…, xn be a sequence of independent normal random variables with parameters (U 1, s2 1), (U2, s2 2),…, (Un, s2n), respectively. In this chapter, different types of change point problems with regard to the mean, variance, and mean and variance are discussed. For simplicity and illustration purposes, we familiarize readers with the three types of changes in the normal sequence by presenting the following three figures, where Figure 2.1 represents a sequence of normal observations with a mean change, Figure 2.2 shows a variance change in the normal observations, and Figure 2.3 indicates a mean and variance change in the sequence of normal observations.
Jie Chen, Arjun K. Gupta
Chapter 3. Multivariate Normal Model
Abstract
In Chapter 2, we have discussed the inferences about change point(s) for a univariate normal model in different situations. In this chapter, we investigate change point(s) problems when the underlying distribution is a multivariate normal distribution.
Jie Chen, Arjun K. Gupta
Chapter 4. Regression Models
Abstract
Regression analysis is an important statistical application employed in many disciplines. Before the introduction of a change point hypothesis into the regression study, the statistician faced problems of being unable to establish a regression model for some observed datasets. If the data structure has changed after a certain point of time, then using one regression model to study the data obviously leaves the data unfitted or leaves them poorly explained by a regression model. Ever since the change point hypothesis was introduced into statistical analyses, the study of switching regression models has taken place in regression analysis. This made some previously poorly fitted regression models better fitted to some datasets after the change point was been located in the regression models.
Jie Chen, Arjun K. Gupta
Chapter 5. Gamma Model
Abstract
In the previous chapters, we introduced the multiple change-point problem for both univariate and multivariate Gaussian models. Now, let us turn our attention away from Gaussian models, and study another important model, the gamma distribution.
Jie Chen, Arjun K. Gupta
Chapter 6. Exponential Model
Abstract
Change point problems occur in various situations and scientific disciplines. In earlier chapters of this monograph, the change point problems associated with the univariate normal, multivariate normal, linear regression, and gamma models were discussed. In this chapter, the change point occurring in an exponential model is studied. An exponential model is useful and appropriate in some experimental sciences, therefore, it is desirable to make an inference about a change point for an exponential model.
Jie Chen, Arjun K. Gupta
Chapter 7. Change Point Model for Hazard Function
Abstract
In the previous chapters, we presented change point analyses for various models. In this chapter, we introduce another change point problem, often encountered in reliability analysis, the problem of estimating the change point in a failure rate or hazard function.
Jie Chen, Arjun K. Gupta
Chapter 8. Discrete Models
Abstract
In previous chapters, we have focused on the change point problems for various continuous probability models. In this chapter we study the change point problem for two discrete probability models, namely, binomial and Poisson models.
Jie Chen, Arjun K. Gupta
Chapter 9. Other Change Point Models
Abstract
Many investigations of change point models consider an abrupt change point or multiple abrupt change points in the parameters of various distributions such as the ones discussed in previous chapters of this monograph. One of the reasons for such consideration is that an abrupt change or multiple abrupt change points are commonly occurring changes in many models across from different disciplines.
Jie Chen, Arjun K. Gupta
Backmatter
Metadaten
Titel
Parametric Statistical Change Point Analysis
verfasst von
Jie Chen
Arjun K. Gupta
Copyright-Jahr
2012
Verlag
Birkhäuser Boston
Electronic ISBN
978-0-8176-4801-5
Print ISBN
978-0-8176-4800-8
DOI
https://doi.org/10.1007/978-0-8176-4801-5

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