Bayesian variable selection in Poisson change-point regression analysis

ABSTRACT

In this article, we develop a Bayesian variable selection method that concerns selection of covariates in the Poisson change-point regression model with both discrete and continuous candidate covariates. Ranging from a null model with no selected covariates to a full model including all covariates, the Bayesian variable selection method searches the entire model space, estimates posterior inclusion probabilities of covariates, and obtains model averaged estimates on coefficients to covariates, while simultaneously estimating a time-varying baseline rate due to change-points. For posterior computation, the Metropolis-Hastings within partially collapsed Gibbs sampler is developed to efficiently fit the Poisson change-point regression model with variable selection. We illustrate the proposed method using simulated and real datasets.

KEYWORDS:

• Bayesian analysis
• Markov chain Monte Carlo
• Partial collapse
• Variable selection
• Varying-dimensional problem

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62F15
• Secondary 62M86

Acknowledgments

This work was supported in part by the Yonsei University Research Grant of 2013 and in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A2056049).