A0152
Title: Jump-size-based Bayesian detection of multiple change-points
Authors: Catherine Liu - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Abstract: An original and general NOn-SEgmental (NOSE) approach is proposed for the detection of multiple change-points. NOSE identifies change-points by the non-negligibility of posterior estimates of the jump heights. Specifically, under the Bayesian paradigm, NOSE treats the step-wise signal as a global infinite dimensional parameter drawn from a proposed process of truncated atomic representation. The random jump heights are further modeled by a Gamma-Indian buffet process shrinkage prior under the form of discrete spike-and-slab. Under the mean-shifted model, the proposed prior elicitation successfully achieves the minimax optimal posterior contraction rate regarding prediction loss. For a bounded number of change-points, NOSE enjoys a lower localization error compared with existing approaches, even in addressing more difficult problems that have a lower signal-to-noise ratio. NOSE is applicable and effective in detecting scale shifts, mean shifts, and structural changes in regression coefficients under linear or autoregression models. Comprehensive simulations and several real-world examples demonstrate the superiority of NOSE in detecting abrupt changes under various data settings. Next, we introduce SBPCPM, an extension of the NOSE approach, which deploys a hypothesis test rather than tackle sparsity and discovers new change-points in a dataset of the London House Index between 2000 and 2022.
