E-values for anytime-valid inference with exponential families

Hao, Y. (2025)

Doctoral Thesis

Traditional hypothesis testing requires researchers to set a fixed sample size in advance. After collecting data, the test determines whether to reject the null hypothesis. In contrast, modern approaches like anytime-valid tests (e.g., methods based on e-values and e-processes) provide greater flexibility. These methods allow researchers to assess evidence continuously as data is gathered, eliminating the need for a pre-determined sample size. E-values, in particular, do not require predefined stopping rules for the experiment. This dissertation focuses on the application of e-values and e-processes within exponential families.

• Hypothesis testing
• E-value
• E-process
• Exponential family
• Large deviation inequality
• K-sample testing
• Anytime-valid sequential testing

• All authors: Hao, Y.
• Supervisor: Grünwald, P.D.
• Co-supervisor: Ly, A.
• Committee: Dickhaus, T.; Ren, Z.; Koning, N.W.; Derks, G.L.A.; Fiocco, M.
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute (MI), Faculty of Science, Leiden University
• Date: 2025-02-18