Advances and Applications in Statistics
Volume 7, Issue 1, Pages 115 - 126
(April 2007)
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A BAYESIAN APPROACH TO THE STATISTICAL ANALYSIS OF A SMOOTH-ABRUPT CHANGE POINT MODEL
Jie Chen (U. S. A.) and A. K. Gupta (U. S. A.)
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Abstract: In this paper, we study a two change points model, consisting of a smooth change followed by an abrupt change. In particular, we call this a smooth-abrupt change point (SACP) model. That is, at an unknown point of time the mean of a sequence of normal random variables starts to change according to a linear trend, and then at another unknown point of time the mean of this sequence drops back to the original one. This is an interesting model that may be encountered in quality control, medicine, genetics studies, and other disciplines. Our goal is to find those two unknown time points at which the changes have taken place. This model has not been studied adequately in the literature. We propose to use a Bayesian approach to detect the changes. Simulation studies of the proposed method are conducted and an application of using the proposed method to find changes in gene expression of the DAL5 gene in the yeast Saccharomyces cerevisiae data set is given. |
Keywords and phrases: change point, smooth-abrupt change point model, posterior distribution, gene expression. |
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