Monitoring a Bernoulli process subject to gradual changes in the success rates of a sequence of Bernoulli random variables

REFERENCES

• Aue, A., and J. Steinebach. 2002. “A Note on Estimating the Change-Point of a Gradually Changing Stochastic Process.” Statistics & Probability Letters 56 (2):177–91. doi:10.1016/S0167-7152(01)00184-5
   Web of Science ®Google Scholar
• Brown, M. 2008. “Monitoring a Poisson Process in Several Categories Subject to Changes in the Arrival Rates.” Statistics & Probability Letters 78 (16):2637–43. doi:10.1016/j.spl.2008.03.005
   Web of Science ®Google Scholar
• Brown, M. 2012. “Detection of Changes in Multinomial Data.” International Journal of Statistics and Probability 1 (2):96–102. doi:10.5539/ijsp.v1n2p96
   Google Scholar
• Brown, M. 2019. “Monitoring a Poisson Process Subject to Gradual Changes in the Arrival Rates.” Sequential Analysis 38 (3):358–68. doi:10.1080/07474946.2019.1648923
   Web of Science ®Google Scholar
• Brown, M. 2021. “Monitoring a Poisson Process Subject to Gradual Changes in the Arrival Rates Where the Arrival Rates Are Unknown.” Sequential Analysis 40 (3):427–40. doi:10.1080/07474946.2021.1940504
   Web of Science ®Google Scholar
• Brown, M., and S. Zacks. 2006. “On the Bayesian Detection of a Change in the Arrival Rate of a Poisson Process Monitored at Discrete Epochs.” International Journal for Statistics and Systems 1:1–13.
   Google Scholar
• Chernoff, H., and S. Zacks. 1964. “Estimating the Current Mean of a Normal Distribution Which Is Subjected to Changes in Time.” The Annals of Mathematical Statistics 35 (3):999–1018. doi:10.1214/aoms/1177700517
   Google Scholar
• Herberts, T., and U. Jensen. 2004. “Optimal Detection of a Change Point in a Poisson Process for Different Observation Schemes.” Scandinavian Journal of Statistics 31 (3):347–66. doi:10.1111/j.1467-9469.2004.02-102.x
   Web of Science ®Google Scholar
• Hinkley, D., and E. Hinkley. 1970. “Inference about the Change-Point in a Sequence of Binomial Variables.” Biometrika 57 (3):477–88. doi:10.1093/biomet/57.3.477
   Web of Science ®Google Scholar
• Page, E. S. 1954. “Continuous Inspection Schemes.” Biometrika 41 (1-2):100–14. doi:10.1093/biomet/41.1-2.100
   Web of Science ®Google Scholar
• Peskir, G., and A. N. Shiryaev. 2002. “Solving the Poisson Disorder Problem.” In Advances in Finance and Stochastics: Essays in Honor of Dieter Sonderman, edited by Klaus Sandmann and Philip J. Schönbucher, 295–312. New York: Springer.
   Google Scholar
• Polunchenko, A., and A. Tartakovsky. 2010. “On the Optimality of the Shiryaev-Roberts Procedure for Detecting a Change in Distribution.” Annals of Statistics 38 (6):3445–57.
   Web of Science ®Google Scholar
• Shewhart, W. A. 1926. “Quality Control Charts.” Bell System Technical Journal 5 (4):593–603. doi:10.1002/j.1538-7305.1926.tb00125.x
   Google Scholar
• Shiryaev, A. N. 1978. Optimal Stopping Rules. Berlin: Springer.
   Google Scholar
• Smith, A. F. M. 1975. “A Bayesian Approach to Inference about a Change-Point in the Sequence of Random Variables.” Biometrika 62 (2):407–16. doi:10.1093/biomet/62.2.407
   Web of Science ®Google Scholar
• Steinebach, J., and H. Timmermann. 2011. “Sequential Testing of Gradual Changes in the Drift of a Stochastic Process).” Journal of Statistical Planning and Inference 141 (8):2682–99. doi:10.1016/j.jspi.2011.02.020
   Web of Science ®Google Scholar
• Tartakovsky, A., B. Rozovskii, R. Blazek, and H. Kim. 2006. “Sequential Change-Point Detection Methods with Applications to Rapid Detection of Intrusions in Information Systems.” Statistical Methodology 3 (3):252–93. doi:10.1016/j.stamet.2005.05.003
   Google Scholar
• Timmermann, H. 2015. “Sequential Detection of Gradual Changes in the Location of a General Stochastic Process.” Statistics & Probability Letters 99:85–93. doi:10.1016/j.spl.2015.01.001
   Web of Science ®Google Scholar
• Vogt, M., and H. Dette. 2015. “Detecting Gradual Changes in Locally Stationary Processes.” The Annals of Statistics 43 (2):713–40. doi:10.1214/14-AOS1297
   Web of Science ®Google Scholar
• Zacks, S. 1983. “Survey of Classical and Bayesian Approaches to the Change-Point Problem: Fixed Sample and Sequential Procedures for Testing and Estimation.” Recent Advances in Statistics 2:245–69.
   Google Scholar
• Zacks, S., and Z. Barzily. 1981. “Bayes Procedures for Detecting a Shirt of the Probability of Success in a Series of Bernoulli Trials.” Journal of Statistical Planning and Inference 5 (2):107–19. doi:10.1016/0378-3758(81)90021-5
   Web of Science ®Google Scholar