Testing by Betting and Borrowing Revisited

Speaker(s)

Yonis Kulane , Yonis Kulane
Location

EUR
Rotterdam

Date and time

June 18, 2025
11:00 - 12:30

We study the betting game introduced by Shafer & Vovk (2005) and used by Wang & Ramdas (2024) to study borrowing in a binary betting game. We first show how this betting game is equivalent to testing with log-optimal e-values where the alternative distribution is implied by the betting strategy. The amount of wealth gambled is directly linked to the implied alternative. We use this insight to generalize betting games with borrowing to non-binary settings. In addition, we assess the statistical impact of borrowing via Monte Carlo simulations. The results of our simulations illustrate that the best performing borrowing strategy is one where long-term liabilities are zero. Borrowing does not lead to long-term effects but might increase evidence in the short run. Finally, we argue that net wealth is a more suitable measure of evidence against a null hypothesis. We also discuss the implications of restricting net wealth to be nonnegative and borrowing on evidence.