Abstract
In this paper, we derive the limit of experiments for one-parameter Ising models on dense regular graphs. In particular, we show that the limiting experiment is Gaussian in the “low temperature” regime, and non-Gaussian in the “critical” regime. We also derive the limiting distributions of the maximum likelihood and maximum pseudolikelihood estimators, and study limiting power for tests of hypothesis against contiguous alternatives. To the best of our knowledge, this is the first attempt at establishing the classical limits of experiments for Ising models (and more generally, Markov random fields).
Funding Statement
The second author was supported in part by NSF Grant DMS-2113414.
Acknowledgments
We thank Nabarun Deb and Rajarshi Mukherjee for helpful comments throughout this project. We also thank Richard Nickl for suggesting this problem. The presentation of the paper greatly benefited from the suggestions of an anonymous referee, and the Associate Editor.
Citation
Yuanzhe Xu. Sumit Mukherjee. "Inference in Ising models on dense regular graphs." Ann. Statist. 51 (3) 1183 - 1206, June 2023. https://doi.org/10.1214/23-AOS2286
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