In many econometrics applications, the dataset under investigation spans heterogeneous regimes that are more appropriately modeled using piece-wise components for each of the data segments separated by change-points. We consider using Bayesian high-dimensional shrinkage priors in a change point setting to understand segment-specific relationship between the response and the covariates. Covariate selection before and after each change point can identify possibly different sets of relevant covariates, while the fully Bayesian approach ensures posterior inference for the change points is also available. We demonstrate the flexibility of the approach for imposing different variable selection constraints like grouping or partial selection and discuss strategies to detect an unknown number of change points. Simulation experiments reveal that this simple approach delivers accurate variable selection, and inference on location of the change points, and substantially outperforms a frequentist lasso-based approach, uniformly across a wide range of scenarios. Application of our model to Minnesota house price dataset reveals change in the relationship between house and stock prices around the sub-prime mortgage crisis.

中文翻译：

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用于变化点分析的贝叶斯高维回归

在许多计量经济学应用中，所研究的数据集跨越了异构体系，对于由变化点分隔的每个数据段，使用分段组件更合适地建模这些体系。我们考虑在变化点设置中使用贝叶斯高维收缩先验来理解响应和协变量之间的特定于段的关系。每个变化点前后的协变量选择可以识别可能不同的相关协变量集，而完全贝叶斯方法确保对变化点的后验推断也是可用的。我们展示了施加不同变量选择约束（如分组或部分选择）的方法的灵活性，并讨论了检测未知数量变化点的策略。仿真实验表明，这种简单的方法提供了准确的变量选择和对变化点位置的推断，并且在广泛的场景中一致地大大优于基于频率论的套索方法。我们的模型在明尼苏达州房价数据集上的应用揭示了次贷危机前后房价和股票价格之间关系的变化。