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

TL;DR

This paper introduces a Bayesian method for high-dimensional change point linear regression, enabling detection of multiple change points and variable selection, demonstrated on Minnesota house price data.

Contribution

It develops a fully Bayesian framework with segment-specific priors for high-dimensional change point regression, including unknown change point detection and variable selection.

Findings

Accurately detects multiple change points in high-dimensional data.

Outperforms homogeneous models in real estate data analysis.

Provides posterior probabilities for variable selection in each segment.

Abstract

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.