INFERENCE IN ISING MODELS ON DENSE REGULAR GRAPHS

• 成果类型: Article
• 署名作者: Xu, Yuanzhe; Mukherjee, Sumit
• 署名单位: Columbia University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2286
• 发表日期: 2023
• 页码: 1183-1206
• 关键词: convergent sequences; Mean-field; fluctuations; statistics

摘要

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 ex-periment is Gaussian in the low temperature regime, and non-Gaussian in the critical regime. We also derive the limiting distributions of the maxi-mum likelihood and maximum pseudolikelihood estimators, and study limit-ing 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).