We propose an original and general NOn-SEgmental (NOSE) approach for the detection of multiple change-points. NOSE identifies change-points by the non-negligibility of posterior estimates of the jump heights. Alternatively, under the Bayesian paradigm, NOSE treats the step-wise signal as a global infinite dimensional parameter drawn from a proposed process of atomic representation, where the random jump heights determine the locations and the number of change-points simultaneously. The random jump heights are further modeled by a Gamma-Indian buffet process shrinkage prior under the form of discrete spike-and-slab. The induced maximum a posteriori estimates of the jump heights are consistent and enjoy zerodiminishing false negative rate in discrimination under a 3-sigma rule. The success of NOSE is guaranteed by the posterior inferential results such as the minimaxity of posterior contraction rate, and posterior consistency of both locations and the number of abrupt changes. NOSE is applicable and effective to detect 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.

翻译：我们提出了一种原创且通用的非分段（NOSE）方法，用于检测多个突变点。NOSE通过跳跃高度的后验估计不可忽略性来识别突变点。在贝叶斯范式下，NOSE将阶梯信号视为全局无限维参数，该参数从所提出的原子表示过程中抽取，其中随机跳跃高度同时决定突变点的位置和数量。随机跳跃高度进一步通过离散的spike-and-slab形式的Gamma-印度自助餐过程收缩先验进行建模。由此得到的跳跃高度最大后验估计具有一致性，并在3-sigma规则下实现零递减的假阴性判别率。NOSE的成功得益于后验推断结果，例如后验收缩率的极小极大性以及突变位置和数量的后验一致性。NOSE可有效检测线性或自回归模型中的尺度偏移、均值偏移以及回归系数的结构性变化。综合仿真和多个实际案例表明，NOSE在不同数据设置下检测突变点具有优越性。