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

For models that can be simulated but whose likelihood cannot be evaluated, SLICE treats fresh simulations under each candidate parameter as references, normalizes the observed score into a conditional e-value, and multiplies these factors into a test martingale that is inverted into an anytime-valid confidence sequence. Validity holds for any positive predictable score, while the score only sets how fast the sequence shrinks; on synthetic benchmarks, a semi-synthetic audit of model routing in an LLM API, and OGLE-IV microlensing data, amortized neural ratio scores come close to exact likelihood ratios and application-specific scores.

For models that can be simulated but whose likelihood cannot be evaluated, SLICE treats fresh simulations under each candidate parameter as references, normalizes the observed score into a conditional e-value, and multiplies these factors into a test martingale that is inverted into an anytime-valid confidence sequence. Validity holds for any positive predictable score, while the score only sets how fast the sequence shrinks; on synthetic benchmarks, a semi-synthetic audit of model routing in an LLM API, and OGLE-IV microlensing data, amortized neural ratio scores come close to exact likelihood ratios and application-specific scores.