A1209
Title: Non-segmental Bayesian detection of multiple change-points
Authors: Chong Zhong - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Zhihua Ma - Shenzhen University (China)
Xu Zhang - South China Normal University (China)
Catherine Liu - The Hong Kong Polytechnic University (Hong Kong)
Abstract: Detection of multiple change points has long been important and active in capturing abrupt change signals within various structures of data streams under wide applications. The common spirit of existing literature is segment-wise in the sense that segment parameters of the local signal on each segment are studied segment-wisely. In contrast, a general and original non-segmental approach is proposed. The pure jump process as a global infinite-dimensional parameter is treated and modelled by an atomic representation where random atoms are associated with random heights. Under the atomic representation, the change-point detection is transferred to discriminating the non-zero outliers from the posterior estimates of the jump sizes at all data points. A class of dynamic discrete spike-and-slab shrinkage priors for the random heights in the global parameter is constructed so that the posterior contraction of the jump sizes attains the optimal minimax rate. An empirical 3-sigma criterion is employed to discriminate non-zero jump sizes, resulting in an asymptotically zero false negative rate. In numerical studies, the approach outperforms existing methods in detecting scale shifts and is competent in detecting mean shifts and structural changes under linear regression or auto-regression settings.
