Year: 2026
Type: preprint
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 $β_Q$ 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.
Source: arXiv (Cornell University)
Institutions: Tsinghua University, Flatiron Institute, Tulane University
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G4170799738, G5534601845
OpenAlex ID: W7224134185