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INFERENCE IN ISING MODELS ON DENSE REGULAR GRAPHS
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DOI：10.1214/23-AOS2286.png)
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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).
Keyword:
Key words and phrases. Ising model
limits of experiments
phase transition
asymptotic power
asymptotic efficiency
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