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arXiv Statistics ML By Stefano Cortinovis, Laura Battaglia, Fran\c{c}ois Caron

SLICE: Sequential Likelihood-Free Inference via Conformal E-Values

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SLICE: Sequential Likelihood-Free Inference via Conformal E-Values introduces a method for constructing exact anytime-valid confidence sequences for parameters of scientific models that can be simulated but have intractable likelihoods. The approach uses fresh simulations at each observation to conformalize a positive predictable score into a conditional e-value, whose product forms a test martingale that is inverted over the parameter space. The method is shown to be valid for any score, with the oracle likelihood-ratio score maximizing expected log growth, and is demonstrated on synthetic benchmarks, an audit of model routing in an LLM API, and microlensing data, where the resulting confidence sequences remain valid under continuous monitoring while neural scores remain competitive with exact likelihood ratios and application-specific scores.

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