On Posterior consistency of Bayesian Changepoint models

02/25/2021
by   Nilabja Guha, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

03/14/2022

Bayesian inference on hierarchical nonlocal priors in generalized linear models

Variable selection methods with nonlocal priors have been widely studied...
07/24/2020

Multinomial Sampling for Hierarchical Change-Point Detection

Bayesian change-point detection, together with latent variable models, a...
05/08/2022

Optimal Change-point Testing for High-dimensional Linear Models with Temporal Dependence

This paper studies change-point testing for high-dimensional linear mode...
04/07/2021

Modeling a sequence of multinomial data with randomly varying probabilities

We consider a sequence of variables having multinomial distribution with...
06/01/2020

On Posterior Consistency of Bayesian Factor Models in High Dimensions

As a principled dimension reduction technique, factor models have been w...
06/09/2021

Ultra High Dimensional Change Point Detection

Structural breaks have been commonly seen in applications. Specifically ...
03/03/2021

Product Partition Dynamic Generalized Linear Models

Detection and modeling of change-points in time-series can be considerab...