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

REFERENCES

• Baron, M. 2002. “Bayes and Asymptotically Pointwise Optimal Stopping Rules for the Detection of Influenza Epidemics.” In Case Studies in Bayesian Statistics, edited by C. Gatsonis, R. E. Kass, A. Carriquiry, A. Gelman, D. Higdon, D. K. Pauler, and I. Verdinelli, Vol. 6, 153–163. New York: Springer.
   Google Scholar
• Baron, M., K. Choudhary, and X. Yu. 2013. “Change-Point Detection in Binomial Thinning Processes, with Applications in Epidemiology.” Sequential Analysis 32 (3): 350–367. https://doi.org/10.1080/07474946.2013.803821
   Web of Science ®Google Scholar
• Chow, Y. S., H. Robbins, and D. Siegmund. 1971. Great Expectations: The Theory of Optimal Stopping. Boston: Houghton Mifflin Company.
   Google Scholar
• Girardin, V., V. Konev, and S. Pergamenchtchikov. 2018. “Kullback-Leibler Approach to CUSUM Quickest Detection Rule for Markovian Time Series.” Sequential Analysis 37 (3): 322–341. https://doi.org/10.1080/07474946.2018.1548846
   Web of Science ®Google Scholar
• Lai, T. L. 1998. “Informations Bounds and Quick Detection of Parameters Changes in Stochastic Systems.” IEEE Transactions on Information Theory 44 (7): 2917–2929.
   Web of Science ®Google Scholar
• Lai, T. L. 2000. “Sequential Multiple Hypothesis Testing and Efficient Fault Detection-Isolation in Stochastic Systems.” IEEE Transactions on Information Theory 46: 595–608.
   Web of Science ®Google Scholar
• Moustakides, G. V. 1986. “Optimal Stopping Times for Detecting Changes in Distributions.” Annals of Statistics 14: 1379–1387.
   Web of Science ®Google Scholar
• Pergamenchtchikov, S. M., and A. G. Tartakovsky. 2018. “Asymptotically Optimal Pointwise and Minimax Quickest Change-Point Detection for Dependent Data.” Statistical Inference for Stochastic Processes 21 (1): 217–259. https://doi.org/10.1007/s11203-016-9149-x
   Google Scholar
• Pergamenchtchikov, S. M., and A. G. Tartakovsky. 2019. “Asymptotically Optimal Pointwise and Minimax Change-Point Detection for General Stochastic Models with a Composite Post-Change Hypothesis.” Journal of Multivariate Analysis 174: 104541. https://doi.org/10.1016/j.jmva.2019.104541
   Web of Science ®Google Scholar
• Pergamenchtchikov, S. M., A. G. Tartakovsky, and V. S. Spivak. 2022. “Minimax and Pointwise Sequential Change-Point Detection and Identification for General Stochastic Models.” Journal of Multivariate Analysis 190: 104977. https://doi.org/10.1016/j.jmva.2022.104977
   Web of Science ®Google Scholar
• Pollak, M., and A. G. Tartakovsky. 2009. “Optimality Properties of the Shiryaev-Roberts Procedure.” Statistica Sinica 19: 1729–1739.
   Web of Science ®Google Scholar
• Shiryaev, A. N. 1973. Statistical Sequential Analysis: Optimal Stopping Rules. Vol. 38. Translations of Mathematical Monographs. Providence, RI: American Mathematical Society.
   Google Scholar
• Shiryaev, A. N. 2008. Optimal Stopping Rules. New York: Springer.
   Google Scholar
• Spitzer, F., H. Kesten, and P. Ney. 1966. “The Galton-Watson Process with Mean One and Finite Variance.” Probability Theory and Its Applications 11: 579–611.
   Google Scholar
• Tartakovsky, A. G. 2020. Sequential Change Detection and Hypothesis Testing: General Non-i.i.d. Stochastic Models and Asymptotically Optimal Rules. Monographs on Statistics and Applied Probability 165. Boca Raton: Chapman & Hall/CRC Press, Taylor & Francis Group.
   Google Scholar
• Tartakovsky, A. G., I. Nikiforov, and M. Basseville. 2015. Sequential Analysis: Hypothesis Testing and Change-Point Detection. New York: Chapman & Hall/CRC.
   Google Scholar
• Tartakovsky, A. G., and V. V. Veeravalli. 2005. “General Asymptotic Bayesian Theory of Quickest Change Detection.” Theory of Probability & Its Applications 49 (3): 458–497. https://doi.org/10.1137/S0040585X97981202
   Web of Science ®Google Scholar
• Yakir, B. 1994. “Optimal Detection of a Change in Distribution When the Observations Form a Markov Chain with a Finite State Space.” Change-Point Problems, IMS Lecture Notes—Monograph Series 23: 346–358.
   Google Scholar
• Yuchen, L., A. G. Tartakovsky, and V. V. Veeravalli. 2023. “Quickest Change Detection with Non-Stationary Post-Change Observations.” IEEE Transactions on Information Theory 69 (5): 3400–3414. https://doi.org/10.1109/TIT.2022.3230583
   Web of Science ®Google Scholar