all AI news
Anytime-valid t-tests and confidence sequences for Gaussian means with unknown variance
April 25, 2024, 7:43 p.m. | Hongjian Wang, Aaditya Ramdas
cs.LG updates on arXiv.org arxiv.org
Abstract: In 1976, Lai constructed a nontrivial confidence sequence for the mean $\mu$ of a Gaussian distribution with unknown variance $\sigma^2$. Curiously, he employed both an improper (right Haar) mixture over $\sigma$ and an improper (flat) mixture over $\mu$. Here, we elaborate carefully on the details of his construction, which use generalized nonintegrable martingales and an extended Ville's inequality. While this does yield a sequential t-test, it does not yield an "e-process" (due to the nonintegrability …
abstract arxiv confidence cs.lg distribution flat math.st mean stat.me stat.ml stat.th tests type variance
More from arxiv.org / cs.LG updates on arXiv.org
The Perception-Robustness Tradeoff in Deterministic Image Restoration
2 days, 4 hours ago |
arxiv.org
Jobs in AI, ML, Big Data
Founding AI Engineer, Agents
@ Occam AI | New York
AI Engineer Intern, Agents
@ Occam AI | US
AI Research Scientist
@ Vara | Berlin, Germany and Remote
Data Architect
@ University of Texas at Austin | Austin, TX
Data ETL Engineer
@ University of Texas at Austin | Austin, TX
Lead GNSS Data Scientist
@ Lurra Systems | Melbourne