  In many applications, the dataset under investigation exhibits heterogeneous
regimes that are more appropriately modeled using piece-wise linear models for
each of the data segments separated by change-points. Although there have been
much work on change point linear regression for the low dimensional case,
high-dimensional change point regression is severely underdeveloped. Motivated
by the analysis of Minnesota House Price Index data, we propose a fully
Bayesian framework for fitting changing linear regression models in
high-dimensional settings. Using segment-specific shrinkage and diffusion
priors, we deliver full posterior inference for the change points and
simultaneously obtain posterior probabilities of variable selection in each
segment via an efficient Gibbs sampler. Additionally, our method can detect an
unknown number of change points and accommodate different variable selection
constraints like grouping or partial selection. We substantiate the accuracy of
our method using simulation experiments for a wide range of scenarios. We apply
our approach for a macro-economic analysis of Minnesota house price index data.
The results strongly favor the change point model over a homogeneous (no change
point) high-dimensional regression model.
