Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means

ArXi:2605.07964v1 Announce Type: cross Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on the choice of martingale updates, and many existing constructions do not exploit prior information about plausible data-generating distributions or mean values. We propose a Bayes-assisted framework that uses a Bayesian working predictive model to adaptively construct confidence sequences.