This study considers the problem of multiple change-points detection. For this problem, we develop an objective Bayesian multiple change-points detection procedure in a normal model with heterogeneous variances. Our Bayesian procedure is based on a combination of binary segmentation and the idea of the screening and ranking algorithm (Niu and Zhang in Ann Appl Stat 6:1306–1326, 2012). Using the screening and ranking algorithm, we can overcome the drawbacks of binary segmentation, as it cannot detect a small segment of structural change in the middle of a large segment or segments of structural changes with small jump magnitude. We propose a detection procedure based on a Bayesian model selection procedure to address this problem in which no subjective input is considered. We construct intrinsic priors for which the Bayes factors and model selection probabilities are well defined. We find that for large sample sizes, our method based on Bayes factors with intrinsic priors is consistent. Moreover, we compare the behavior of the proposed multiple change-points detection procedure with existing methods through a simulation study and two real data examples.

这项研究考虑了多个变化点检测的问题。针对此问题，我们在具有异质方差的正常模型中开发了客观的贝叶斯多变化点检测程序。我们的贝叶斯程序基于二进制分割和筛选和排序算法思想的组合（Niu和Zhang，Ann Appl Stat 6：1306–1326，2012）。使用筛选和排序算法，我们可以克服二进制分割的缺点，因为它无法检测到大片段中间的一小部分结构变化或跳跃幅度小的结构变化。我们提出了一种基于贝叶斯模型选择过程的检测过程，以解决没有考虑主观输入的问题。我们构造内在先验，贝叶斯因子和模型选择概率均已定义。我们发现，对于大样本量，我们基于具有固有先验的贝叶斯因子的方法是一致的。此外，我们通过模拟研究和两个实际数据示例，比较了所提出的多变化点检测程序与现有方法的行为。