Semi-parametric Bayesian change-point model based on the Dirichlet process

TL;DR

This paper introduces a semi-parametric Bayesian change-point model utilizing the Dirichlet process, capable of estimating the number of change points dynamically, and demonstrates its effectiveness through simulations and real data applications.

Contribution

It presents a novel Bayesian change-point model that treats the number of change points as a random variable and employs a Dirichlet process for flexible modeling.

Findings

Accurately recovers change points and parameters in simulated data.

Shows improved change point detection over existing models.

Results on real datasets align with previous studies.

Abstract

In this work we introduce a semi-parametric Bayesian change-point model, defining its time dynamic as a latent Markov process based on the Dirichlet process. We treat the number of change point as a random variable and we estimate it during model fitting. Posterior inference is carried out using a Markov chain Monte Carlo algorithm based on a marginalized version of the proposed model. The model is illustrated using simulated examples and two real datasets, namely the coal- mining disasters, that is a widely used dataset for illustrative purpose, and a dataset of indoor radon recordings. With the simulated examples we show that the model is able to recover the parameters and number of change points, and we compare our results with the ones of the-state- of-the-art models, showing a clear improvement in terms of change points identification. The results obtained on the coal-mining disasters and radon data are coherent with previous literature.