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

2026-05-11 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Research Methodology & Innovation · Depth: Expert, extended

Summary

Researchers from the University of Oxford have introduced a Bayes-assisted framework for constructing time-uniform confidence sequences (CSs) for the mean of bounded independent and identically distributed (IID) observations. This framework addresses the practical efficiency limitations of existing CS methods, which often do not incorporate prior information. The proposed approach uses a Bayesian working predictive model to adaptively select martingale updates, maximizing predictive expected log-growth while preserving validity even if the prior or working model is misspecified. The method is proven to be asymptotically log-optimal if the predictive distribution is Wasserstein-consistent, matching the per-sample log-growth of an oracle procedure. The framework is instantiated using robust predictives like Dirichlet-process mixtures and Bayesian exponentially tilted empirical likelihood (BETEL/RETEL). Experiments on synthetic data, sequential best-arm identification for LLM evaluation, and prediction-powered inference demonstrate that informative priors can substantially reduce CS width and sampling effort while maintaining anytime-valid coverage.

Key takeaway

For AI Scientists and Research Scientists developing sequential inference systems, this Bayes-assisted framework offers a robust way to improve the efficiency of confidence sequences. You can significantly reduce the width of your confidence sequences and the required sampling effort by incorporating informative prior knowledge, even if your working model is not perfectly specified. This allows for faster, more precise anytime-valid decisions in applications like LLM evaluation or prediction-powered inference, without compromising statistical guarantees.

Key insights

Bayes-assisted confidence sequences leverage prior information for efficiency without sacrificing anytime-valid coverage.

Principles

• Validity is separate from efficiency.
• Wasserstein-consistent predictives ensure log-optimality.
• Informative priors reduce confidence sequence width.

Method

A Bayesian working predictive distribution selects one-step martingale factors by maximizing predictive expected log-growth, ensuring validity even with misspecified models or priors.

In practice

• Apply to sequential best-arm identification for LLM evaluation.
• Use for prediction-powered inference in bounded mean estimation.
• Consider mixture Dirichlet-process or BETEL/RETEL predictives.

Topics

• Confidence Sequences
• Bayes-Assisted Methods
• Test Martingales
• Asymptotic Log-Optimality
• Wasserstein Consistency

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.