On Posterior consistency of Bayesian Changepoint models

TL;DR

This paper develops a hierarchical Bayesian model for detecting change points and relevant covariates in time series data, providing theoretical guarantees of posterior consistency and demonstrating practical effectiveness.

Contribution

It introduces a novel Bayesian approach with adaptive priors for joint change point detection and covariate selection, with rigorous theoretical analysis and efficient computation.

Findings

Consistent detection of true change points and covariates with high probability.

Effective Gibbs sampling algorithm for practical implementation.

Successful application to crime forecasting data.

Abstract

While there have been a lot of recent developments in the context of Bayesian model selection and variable selection for high dimensional linear models, there is not much work in the presence of change point in literature, unlike the frequentist counterpart. We consider a hierarchical Bayesian linear model where the active set of covariates that affects the observations through a mean model can vary between different time segments. Such structure may arise in social sciences/ economic sciences, such as sudden change of house price based on external economic factor, crime rate changes based on social and built-environment factors, and others. Using an appropriate adaptive prior, we outline the development of a hierarchical Bayesian methodology that can select the true change point as well as the true covariates, with high probability. We provide the first detailed theoretical analysis for posterior consistency with or without covariates, under suitable conditions. Gibbs sampling techniques provide an efficient computational strategy. We also consider small sample simulation study as well as application to crime forecasting applications.