We show that the two-stage minimum description length (MDL) criterion widely used to estimate linear change-point (CP) models corresponds to the marginal likelihood of a Bayesian model with a specific class of prior distributions. This allows results from the frequentist and Bayesian paradigms to be bridged together. Thanks to this link, one can rely on the consistency of the number and locations of the estimated CPs and the computational efficiency of frequentist methods, and obtain a probability of observing a CP at a given time, compute model posterior probabilities, and select or combine CP methods via Bayesian posteriors. Furthermore, we adapt several CP methods to take advantage of the MDL probabilistic representation. Based on simulated data, we show that the adapted CP methods can improve structural break detection compared to state-of-the-art approaches. Finally, we empirically illustrate the usefulness of combining CP detection methods when dealing with long time series and forecasting.

翻译：我们证明，广泛用于估计线性变点模型的两阶段最小描述长度准则，对应于具有特定先验分布类别的贝叶斯模型的边际似然。这一发现使得频率学派与贝叶斯范式的结果得以衔接。借助这一联系，研究者既能依赖变点数量与位置估计的相合性以及频率学派方法的计算高效性，又能获取特定时间点出现变点的概率、计算模型后验概率，并基于贝叶斯后验选择或组合多种变点方法。此外，我们改进了多种变点方法以利用MDL概率表示的优势。基于模拟数据的实验表明，改进后的变点方法相比现有技术能更有效地检测结构性断点。最后，我们通过实证展示了在处理长时序数据与预测任务时组合变点检测方法的实用性。