  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.
