Likelihood-free inference with nuisance parameters through normalizing flows
Researchers decompose normalizing flows to derive near-pivotal statistics for likelihood-free inference with nuisance parameters, recovering the t-test and beating Welch limits.
A new paper decomposes neural-network normalizing flows to uncover pivotal statistics in the presence of nuisance parameters using only a sample generator from the distribution of interest. The statistic is near-pivotal in the sense of minimum average KL-divergence of its p-values and can incorporate prior knowledge of group invariances such as translation and scale. Experiments show it recovers the one-sample t-test almost exactly, outperforms the Welch test on worst-case size over a constrained variance-ratio range, and delivers higher power and much faster runtime than profile likelihood-ratio techniques on small-to-moderate samples.
- Derives near-pivotal statistics from normalizing flows without likelihoods.
- Recovers the one-sample t-test almost exactly.
- Beats Welch test on worst-case size over constrained variance ratios.
- Higher power and faster on small-to-moderate samples than profile likelihood-ratio methods.
Full article139 words · extracted from arxiv.org · click to collapse
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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.10534