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.
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BibTeX
@article{pchelintsev2026truncated,
title = {{Truncated sequential change-point detection for Markov chains with applications in the epidemic statistical analysis}},
author = {Evgenii A Pchelintsev and Serguei Pergamenchtchikov and Roman O Tenzin},
journal = {Sequential Analysis},
year = {2026},
month = sep,
doi = {10.1080/07474946.2023.2285777},
url = {https://hal.science/hal-05723580v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Truncated sequential change-point detection for Markov chains with applications in the epidemic statistical analysis
AU - Evgenii A Pchelintsev
AU - Serguei Pergamenchtchikov
AU - Roman O Tenzin
PY - 2026
DA - 2026/09/07
JO - Sequential Analysis
DO - 10.1080/07474946.2023.2285777
UR - https://hal.science/hal-05723580v1
AB - 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.
SN - 0747-4946
SN - 1532-4176
ER -