Date of Award
2025
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
Committee Chair
Satyaki Roy
Committee Member
Daniel Bossaller
Committee Member
Dongsheng Wu
Research Advisor
Satyaki Roy
Subject(s)
Change-point problems, Poisson processes, Sequential analysis, Mathematical statistics
Abstract
Sequential testing reduces sample size and costs compared to fixed-sample approaches by allowing decision making during data collection. This thesis investigates sequential methods for Poisson processes and change-point detection. Wald’s sequential probability ratio test (SPRT) and efficiency measures are developed. Practical applications of the SPRT are studied, from detecting noisy sources to classification algorithms. The MaxSPRT is derived, and its critical value algorithm is optimized. The MaxSPRT, a Bayesian SPRT, Wilk’s generalized likelihood ratio test, and the Cash statistic are examined. Various change-point algorithms are surveyed, including Shewhart control charts, cumulative sum methods, homogeneity tests, and multiple change-point approaches. These are compared via the Nile River dataset, a Poisson example, and an online change-point detection implementation. Alpha spending functions are compared for their impact on sequential testing and mitigation of false alarms due to repeated hypothesis testing. Future research will investigate Poisson and Bayesian-based sequential analysis and change-point algorithms.
Recommended Citation
Johnson, Samuel, "Evaluating sequential inference via Poisson and change-point frameworks" (2025). Theses. 782.
https://louis.uah.edu/uah-theses/782