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In many applications, the dataset under investigation exhibits heterogeneousregimes that are more appropriately modeled using piece-wise linear models foreach of the data segments separated by change-points. Although there have beenmuch work on change point linear regression for the low dimensional case,high-dimensional change point regression is severely underdeveloped. Motivatedby the analysis of Minnesota House Price Index data, we propose a fullyBayesian framework for fitting changing linear regression models inhigh-dimensional settings. Using segment-specific shrinkage and diffusionpriors, we deliver full posterior inference for the change points andsimultaneously obtain posterior probabilities of variable selection in eachsegment via an efficient Gibbs sampler. Additionally, our method can detect anunknown number of change points and accommodate different variable selectionconstraints like grouping or partial selection. We substantiate the accuracy ofour method using simulation experiments for a wide range of scenarios. We applyour approach for a macro-economic analysis of Minnesota house price index data.The results strongly favor the change point model over a homogeneous (no changepoint) high-dimensional regression model.

Bayesian Inference for High Dimensional Changing Linear Regression with Application to Minnesota House Price Index Data