利用 normalizing flow 在含 nuisance parameters 情形下进行无似然推断

Statistics > Methodology arXiv:2609.10534v1 (stat) [Submitted on 9 Sep 2026] Title:Likelihood-free inference with nuisance parameters through normalizing flows Authors:Phil Assheton View a PDF of the paper titled Likelihood-free inference with nuisance parameters through normalizing flows, by Phil Assheton View PDF HTML (experimental) Abstract: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. Comments: Subjects: Methodology (stat.ME); Machine Learning (cs.LG); Machine Learning (stat.ML) Cite as: arXiv:2609.10534 [stat.ME] (or arXiv:2609.10534v1 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2609.10534 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Phil Assheton [view email] [v1] Wed, 9 Sep 2026 17:58:15 UTC (4,537 KB) Full-text links: Access Paper: View a PDF of the paper titled Likelihood-free inference with nuisance parameters through normalizing flows, by Phil Assheton View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME new | recent | 2026-09 Change to browse by: cs cs.LG stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)