Adaptive resources allocation CUSUM for binomial count data monitoring with application to COVID-19 hotspot detection

Abstract

In this paper, we present an efficient statistical method (denoted as ‘Adaptive Resources Allocation CUSUM’) to robustly and efficiently detect the hotspot with limited sampling resources. Our main idea is to combine the multi-arm bandit (MAB) and change-point detection methods to balance the exploration and exploitation of resource allocation for hotspot detection. Further, a Bayesian weighted update is used to update the posterior distribution of the infection rate. Then, the upper confidence bound (UCB) is used for resource allocation and planning. Finally, CUSUM monitoring statistics to detect the change point as well as the change location. For performance evaluation, we compare the performance of the proposed method with several benchmark methods in the literature and showed the proposed algorithm is able to achieve a lower detection delay and higher detection precision. Finally, this method is applied to hotspot detection in a real case study of county-level daily positive COVID-19 cases in Washington State WA) and demonstrates the effectiveness with very limited distributed samples.

Keywords:

• Multi-arm bandit
• change point detection
• adaptive resources allocation
• count data
• CUSUM statistics

Mathematics subject classifications:

• 62P10
• 62L15

Acknowledgments

The authors are grateful to the Editor, Dr. Jie Chen, the Associate Editor, and anonymous reviewers for their constructive comments that greatly improved the quality of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

H. Yan was supported in part by NSF grant [DMS-1830363]. Y. Mei was supported in part by NSF grant [DMS-2015405]. S. E. Holte's research was supported in part by NSF grant [DMS-1830372] and an NIH grant [AI027757]. In addition, this research was supported in part by an NIH grant [R21 AI157618]. The content is solely the responsibility of the authors and does not necessarily represent.