Likelihood-Free Inference with Nuisance Parameters via Normalizing Flows

Handling nuisance parameters in likelihood-free settings typically requires expensive profile likelihood approximations. This work introduces a structural decomposition of normalizing flows that extracts near-pivotal statistics directly from simulation samples by minimizing the KL-divergence of p-values against uniformity. The architecture integrates group invariances such as scale and translation. Across experiments, it accurately rediscovers the classical one-sample t-test, surpasses the Welch test in worst-case size under constrained variance ratios, and provides higher statistical power alongside faster computation on small-to-moderate sample sizes.