Phase Transitions in Mismatched Bayesian Inference for the Ising Model
Abstract
Bayesian inference with a mismatched model can develop an overconfident phase, characterized by posterior agreement without faithful reconstruction of the true state. We study Bayesian inference from noisy bond measurements of an Ising model in its paramagnetic phase, with true inverse temperature β and measurement-noise strength Δ, while inference assumes corresponding parameters βQ and ΔQ. Using replica field theory, we analytically show that the overconfidence phase can occur when inference underestimates the measurement noise (ΔQ < Δ) or assumes a lower prior temperature than the true one (βQ > β). An exact change of variables maps the problem to a correlated random-bond Ising model, where the informative, uninformative, and overconfident phases correspond to ferromagnetic, paramagnetic, and spin-glass phases, respectively. We further perform Monte Carlo simulations of the mapped model in three dimensions and establish a finite overconfident region between the informative and uninformative phases, consistent with our analytical prediction. Finally, we show that the true model parameters can be inferred directly from the measurement records, providing a natural route to calibrating the inference model.
Related
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BibTeX
@misc{sun2026phase,
title = {{Phase Transitions in Mismatched Bayesian Inference for the Ising Model}},
author = {Xinyu Sun and Zhou-Quan Wan and Shao-Kai Jian and Hong Yao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36041},
eprint = {2610.36041},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36041},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phase Transitions in Mismatched Bayesian Inference for the Ising Model
AU - Xinyu Sun
AU - Zhou-Quan Wan
AU - Shao-Kai Jian
AU - Hong Yao
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36041
UR - https://arxiv.org/abs/2610.36041
AB - Bayesian inference with a mismatched model can develop an overconfident phase, characterized by posterior agreement without faithful reconstruction of the true state. We study Bayesian inference from noisy bond measurements of an Ising model in its paramagnetic phase, with true inverse temperature β and measurement-noise strength Δ, while inference assumes corresponding parameters β_Q and Δ_Q. Using replica field theory, we analytically show that the overconfidence phase can occur when inference underestimates the measurement noise (Δ_Q < Δ) or assumes a lower prior temperature than the true one (β_Q > β). An exact change of variables maps the problem to a correlated random-bond Ising model, where the informative, uninformative, and overconfident phases correspond to ferromagnetic, paramagnetic, and spin-glass phases, respectively. We further perform Monte Carlo simulations of the mapped model in three dimensions and establish a finite overconfident region between the informative and uninformative phases, consistent with our analytical prediction. Finally, we show that the true model parameters can be inferred directly from the measurement records, providing a natural route to calibrating the inference model.
ER -