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WE introduce EPICSCORE, a model-agnostic method that enhances conformal prediction by integrating epistemic uncertainty. Compatible with any Bayesian model and maintaining distribution-free guarantees, EPICSCORE adapts prediction intervals based on data availability, achieving both finite-sample marginal and asymptotic conditional coverage.

We introduce Likelihood-Free Frequentist Inference (LF2I), a framework that bridges classical statistics and machine learning for valid confidence sets in complex, likelihood-free settings. LF2I provides confidence sets with near finite-sample validity and offers practical diagnostics for empirical coverage, ensuring reliable scientific inference without costly Monte Carlo or bootstrap methods.

The paper introduces a novel approach to classifying events under generalized label shift by framing classification as hypothesis testing, which leads to valid uncertainty quantification. This is demonstrated through applications in biology and astroparticle physics.