Li, Li, and Dai's Contribution to the Discussion of "Estimating Means of Bounded Random Variables by Betting" by Waudby-Smith and Aaditya Ramdas

TL;DR

This paper discusses the contributions of Li, Li, and Dai to the work by Waudby-Smith and Ramdas on confidence intervals for bounded data, emphasizing their numerical comparisons and methodological insights.

Contribution

It provides an analysis of Li, Li, and Dai's commentary on the original work, highlighting their numerical comparisons and methodological perspectives.

Findings

Numerical comparisons of different confidence interval methods.

Insights into the use of composite nonnegative martingales.

Discussion on the connection to game-theoretic probability.

Abstract

We congratulate Waudby-Smith and Ramdas for their interesting paper \cite{waudbysmith2022estimating} in generating confidence intervals and time-uniform confidence sequences for mean estimation with bounded observations. Their methodology utilizes composite nonnegative martingales and establishes a connection to game-theoretic probability. Our comments will focus on numerical comparisons with alternative methods.