Truncated sequential change-point detection for Markov chains with applications in the epidemic statistical analysis

Abstract

In this study, we consider disorder detection problems for statistical models with dependent observations defined by Markov chains in a Bayesian setting for a uniform prior distribution when the number of observations is limited by some known quantity. To achieve this, a new optimal sequential detection procedure is constructed using optimal stopping methods. This procedure minimizes the average delay time in the class of sequential procedures with false alarm probabilities that do not exceed a fixed value. The main difference between the proposed detection procedure and the conventional ones is that it is based not on the posterior probabilities but on the weighted Shiryaev-Roberts statistic. This allows for optimal detection in a nonasymptotic sense over any bounded time interval. Thereafter, we applied the constructed procedures to the early detection problem for the beginning of the epidemic spread. We used two epidemic models: the binomial model proposed by Baron, Choudhary, and Yu (2013) and the model based on the Gaussian approximation introduced by Pergamenchtchikov, Tartakovsky, and Spivak (2022). The theoretical results were confirmed through numerical simulations using the Monte Carlo method.

Keywords:

• Bayes detection procedures
• change point Markov models
• Markov epidemic models
• optimal stopping
• sequential detection

Subject Classifications:

• Primary 62L10
• 62L15
• Secondary 60G40
• 60J05
• 60J20

ACKNOWLEDGMENTS

The authors are grateful to the Associate Editor and reviewers for their insightful and constructive comments, which significantly improved the presentation and content of the article.

DISCLOSURE

The authors have no conflicts of interest to report.

Additional information

Funding

This work is supported by RSF Grant No. 22-21-00302 (National Research Tomsk State University, Russia).