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, non Gaussian in the critical regime, and an infinite collection of Gaussians in the high temperature regime. We also derive the limiting distributions of the maximum likelihood and maximum pseudo-likelihood estimators, and study limiting power for tests of hypothesis against contiguous alternatives (whose scaling changes across the regimes). 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).

翻译：本文推导了密集正则图上单参数伊辛模型的实验极限。具体地，我们证明在低温区域极限实验是高斯分布，在临界区域是非高斯分布，而在高温区域则是无穷多个高斯分布的集合。我们还推导了极大似然估计与极大伪似然估计的极限分布，并研究了针对邻接备择假设（其缩放尺度随区域变化）的检验极限功效。据我们所知，这是首次尝试建立伊辛模型（以及更广泛地，马尔可夫随机场）的经典实验极限。