Robust Bayesian Non-segmental Detection of Multiple Change-points
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Change-points detection has long been important and active research areas with broad application in economics, medical research, genetics, social science, etc. It includes themes of the number, locations, and jump sizes of change-points. However, most existing methods focus on segment parameters or features, regardless of Bayesian or frequentist. We propose an innovative non-segmental approach to detect multiple change-points by concentrating the abrupt changes into a global distributional parameter, which is characterized by a function of states of the system. We construct a class of discrete spike and Cauchy-slab variate prior, which distinguishes from existing such two-group mixture priors by a dynamic rate of a latent indicator. A 3-sigma discrimination criterion of change-points is built with sigma being the standard deviation of the sequence of differences between marginal maximum a posteriori estimates on two adjacent discretized states. It intrinsically guarantees reasonable false positive rate to prevent over-detection. The proposed method is powerful and robust to unveil structure changes of the autoregression model for house prices in London and the linear regression model for age-specific fertility in US, not to mention consistent detection results of shifts of mean or scale on known data sets. Abundant simulations demonstrate that the proposed method outperforms state-of-the-art others in finite-sample performance. An R package is developed for detecting changes in mean, scale, and the regression or autocorrelation coefficient.
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