B0286
Title: Sequential tests with extended nonnegative supermartingales: A frequentist approach to improper priors
Authors: Aaditya Ramdas - Carnegie Mellon University (United States)
Hongjian Wang - Carnegie Mellon University (United States) [presenting]
Abstract: Some commonalities and differences are first examined between Bayesian inference and game-theoretic approaches to anytime-valid inference. These include the prior-posterior ratio martingale and the universal inference approach. The central contribution is a new frequentist treatment of improper priors. The main technical development is a new theory of nonnegative martingales that may not be integrable (like a likelihood mixed with an improper prior). Using a device called the extended Ville's inequality, confidence sequences and sequential tests are developed using extended supermartingales and e-processes. A simple example goes back to a prior study, which used the flat prior to mixing over an unknown Gaussian mean. The theory greatly expands the scope of their ideas, including nonparametric settings.
