Bayesian change-points detection assuming a power law process in the recurrent-event context

Abstract

This article establishes a Bayesian framework to detect the number and values of change-points in the recurrent-event context with multiple sampling units, where the observation times of the sampling units can vary. The event counts are assumed to be a non-homogeneous Poisson process with the Weibull intensity function, that is, a power law process. We fit models with different numbers of change-points, use the Markov chain Monte Carlo method to sample from the posterior, and employ the Bayes factor for model selection. Simulation studies are conducted to check the estimation accuracy, precision, and model selection performance, as well as to compare the model selection performance of the Bayes factor and the deviance information criterion under different scenarios. The simulation studies show that the proposed methodology estimates the change-points and the power law process parameters with high accuracy and precision. The proposed framework is applied to two case studies and yields sensible results. The power law process is flexible and the proposed framework is practically useful in many fields—reliability analysis in engineering, pharmaceutical studies, and travel safety, to name a few.

Keywords:

• Bayes factor
• criterion comparison
• model selection
• non-homogeneous Poisson process

Acknowledgments

We would like to thank Dr. Coelho-Barros, the coauthor of Achcar, Coelho-Barros, and de Souza (2016) who provided the R2jags code for their paper. Thanks to Dr. Dibley who gave us the permission to use his data. Sincere thanks to Dr. Frobish who provided the ARI study data and whose change-point research greatly inspired our work. We would also like to thank Mike Cammilleri, the Director of IT Office at the University of Wisconsin-Madison for providing support in high-performance computing. In addition, we would like to thank the reviewers for the constructive comments that help us improve the paper.