Bayes with No Shame: Admissibility Geometries of Predictive Inference

arXiv:2603.05335 · stat.ML, cs.LG, math.ST, stat.TH · Submitted 2026-03-05 · Read on arXiv

stat.ML, cs.LG, math.ST, stat.TH

Submitted: 2026-03-05

Updated: 2026-08-27

Terminology

• Admissibility — 90× in this paper · explained in 2 episodes
• Calibration — 37× in this paper · explained in 7 episodes
• Exchangeability — 13× in this paper · explained in 2 episodes
• Conformal Prediction — 11× in this paper · explained in 5 episodes
• Consistency — 7× in this paper · explained in 3 episodes
• Steering — 6× in this paper · explained in 2 episodes
• Self-consistency — 4× in this paper · explained in 2 episodes
• Loss Function — 3× in this paper · explained in 2 episodes
• Regret — 3× in this paper · explained in 3 episodes
• Action Space — 2× in this paper · explained in 1 episode
• Annual Conference on Learning Theory — 2× in this paper
• Covariate Shift — 2× in this paper · explained in 2 episodes
• Large Language Models (LLMs) — 1× in this paper · explained in 6 episodes
• Predictive Modeling — 1× in this paper · explained in 2 episodes
• Probabilistic Forecasting — 1× in this paper · explained in 3 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• Safe Testing
• De Finetti + Sanov = Bayes: Exchangeable Prediction under Moment Constraints
• Entropy-Regularized Inference: A Predictive Approach
• Martingale Posterior Predictive Coherence: Hausdorff Moment Hierarchy
• Bayes, E-values and Testing
• Admissible anytime-valid sequential inference must rely on nonnegative martingales

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