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Life sciences · Preprint
arXiv · September 9, 2026
Raises a question worth testing. It does not answer one.
This preprint describes a neural-network-based statistical method for likelihood-free inference that aims to identify near-pivotal statistics in the presence of nuisance parameters. The approach is demonstrated on simulated benchmarks (one-sample t-test, Welch test, partial biserial correlations) but has not undergone peer review and lacks validation on real-world data or in applied scientific contexts.
Preprint. Intervention: Neural-network-based normalizing flow decomposition for discovery of near-pivotal statistics. Compared with: Welch test, profile likelihood-ratio techniques.
Method discovers the one-sample t-test 'almost exactly' in simulation Outperforms Welch test in worst-case size over a constrained variance-ratio range Achieves good calibration on partial biserial correlations
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This is a methodological development paper presenting a novel statistical technique without empirical validation on real clinical or scientific data; it demonstrates proof-of-concept through simulations and toy examples rather than answering a clinical question.
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We present a simple decomposition of a neural-network-based normalizing flow that naturally uncovers a pivotal statistic (or something close) in the presence of nuisance parameters, based only on a sample generator from the distribution of interest. We show that the statistic is near-pivotal in the sense of minimum average KL-divergence of its $p$-values versus uniform and we argue that it can be expected to have good power when the dimension of the statistic equals the dimension of the parameter. It is able to incorporate prior knowledge about group invariances such as translation and scale. It can discover the one-sample $t$-test almost exactly, outperforms the Welch test in terms of worst-case size over a constrained variance-ratio range and achieves good calibration on partial biserial correlations, while showing higher power (and being much faster) on small-to-moderate samples than profile likelihood-ratio techniques.
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