论文标题
非段贝叶斯对多个变更点的检测
Non-segmental Bayesian Detection of Multiple Change-points
论文作者
论文摘要
我们提出了一种原始和一般的非段（鼻）方法，以检测多个变更点。鼻子通过跳高高度后验估计值的不可分析来识别变化点。或者，在贝叶斯范式下，鼻子将逐步信号视为从所提出的原子表示过程中绘制的全局无限尺寸参数，其中随机跳跃高度同时确定位置和变化点的数量。在离散的尖峰和slab的形式下，随机跳跃高度通过伽马 - 印度自助餐过程收缩进一步建模。诱导的最大值跳高高度的后验估计是一致的，并且在3- sigma规则下的歧视中享受奇数型假阴性率。鼻子的成功是通过后推断结果保证的，例如后部收缩率的最小程度，以及位置的后验一致性和突然变化的数量。鼻子适用且有效地检测尺度的偏移，平均移位以及线性或自动降低模型下回归系数的结构变化。全面的模拟和几个现实世界的例子表明，在各种数据设置下检测突然变化时，鼻子的优势。
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.
