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.
From the original article
1 min read at arxiv.orgWe 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.
By Phil Assheton · arxiv.org
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