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

Many scientific models can be simulated but have intractable likelihoods, making frequentist uncertainty quantification difficult. We construct exact anytime-valid confidence sequences for parameters of such models. At each observation, fresh simulations from each candidate null conformalize a positive predictable score into a conditional e-value; multiplying these e-values yields a test martingale that can be inverted over the parameter. Validity therefore holds for any positive predictable score, independently of its accuracy. We show that the oracle likelihood-ratio score maximizes expected log growth, motivating its approximation by an amortized neural ratio estimator. In Gaussian and likelihood-intractable $g$-and-$k$ experiments, the resulting confidence sequences are nearly indistinguishable in width from those based on exact likelihood ratios.