A latent process approach to change-point detection of mixed-type observations

Abstract

Mixed-type observations, such as continuous measurements, discrete counts, and binary outcomes, are commonly present in many applications. The change-point detection with mixed-type observations is challenging since it is difficult to quantify the hidden association among mixed-type observations. In this work, we propose a latent process method to model the mixed observations in a joint manner, and effectively detect the changes. Bayesian parameter estimation and inference are developed for the proposed method by combining the discrete particle filter (DPF) and sequential Monte Carlo (SMC) algorithms. Such an algorithm can efficiently update the high dimensional proposal distribution and can exploit the discrete and continuous natures of the latent processes simultaneously. The performance of the proposed method is illustrated by several numerical examples and a case study of civil-unrest data.

Keywords:

• Bayesian inference
• discrete particle filter
• latent process approach
• mixed-type observations
• sequential Monte Carlo

Acknowledgments

The authors would like to thank the editors and referees for their valuable comments.

Additional information

Funding

This work is partially supported by NIH-R01-GM109718, NSF-CMMI-1916670, NCF-CMMI-1435996, and NSF CISE Expedition (CCF-1918770).

Notes on contributors

Shuyu Chu

Shuyu Chu is a Ph.D. Student in the Department of Statistics at Virginia Tech. Her research interests include change-point detection and modeling complex data.

Xueying Liu

Xueying Liu is a Ph.D. Student in the Department of Statistics at Virginia Tech. Her research interests focus on uncertainty quantification and big data analytics.

Achla Marathe

Achla Marathe is a professor at the Biocomplexity Institute and at the Department of Public Health Sciences, School of Medicine, at the University of Virginia. Her research interest include health economics, social epidemiology, data driven modeling of socially coupled systems, and energy markets.

Xinwei Deng

Xinwei Deng is a Professor of Statistics and Data Science Faculty Fellow at Virginia Tech. His research interest focus on modeling and analysis of data with complex structures, machine learning, design of experiments, and uncertainty quantification.