Inference in Ising models on dense regular graphs
The Annals of Statistics · 2023 · Volume 51 · Issue 3
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).
Keywords
62E20, 62F05, 62F12, 62H22, Asymptotic efficiency, asymptotic power, Ising model, limits of experiments, phase transition
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