Few Trials, Many Metrics: Beta Mixtures for Low-Budget AI Evaluation

arXiv cs.AINovember 3, 2026en

arXiv cs.AI

AI Global Wire

arXiv:2611.00474v1 Announce Type: new Abstract: Evaluating a stochastic AI system often requires many repeated samples per instance, especially for metrics defined over long horizons. Recent work has shown that modeling instance-level success probabilities with a Beta distribution recovers Pass@$k$ from far fewer samples than direct estimation. We show that this framework supports a broader range of evaluation targets. We fit a mixture of Beta distributions by marginal maximum likelihood, with the number of components chosen by BIC. From that one fit, we compute Pass$^k$ and AUC@$k$ at any horizon in closed form. We also derive delta-method confidence intervals for these metrics and for Pass

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